{"id":7,"date":"2020-01-10T18:47:33","date_gmt":"2020-01-10T18:47:33","guid":{"rendered":"https:\/\/mauromaggioni.duckdns.org\/?page_id=7"},"modified":"2021-02-05T15:33:44","modified_gmt":"2021-02-05T15:33:44","slug":"publications","status":"publish","type":"page","link":"https:\/\/mauromaggioni.duckdns.org\/?page_id=7","title":{"rendered":"Publications"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"7\" class=\"elementor elementor-7\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-15bbc1e elementor-section-full_width elementor-section-stretched elementor-section-height-default elementor-section-height-default\" data-id=\"15bbc1e\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;stretch_section&quot;:&quot;section-stretched&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-33626098\" data-id=\"33626098\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-121927d8 elementor-widget elementor-widget-text-editor\" data-id=\"121927d8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><div class=\"teachpress_cloud\"><span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=4&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"7 Publications\" class=\"\">Active Learning<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"11 Publications\" class=\"\">agent-based models<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=3&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"14 Publications\" class=\"\">Clustering<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=9&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"4 Publications\" class=\"\">dictionary learning<\/a><\/span> <span style=\"font-size:14px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"35 Publications\" class=\"\">diffusion geometry<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=50&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"5 Publications\" class=\"\">diffusion wavelets<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=57&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"4 Publications\" class=\"\">digital twins<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=49&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"13 Publications\" class=\"\">geometric wavelets<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=28&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"5 Publications\" class=\"\">harmonic analysis<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=38&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"4 Publications\" class=\"\">heat kernels<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=35&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"12 Publications\" class=\"\">hyperspectral imaging<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"16 Publications\" class=\"\">imaging<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"12 Publications\" class=\"\">interacting particle systems<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"11 Publications\" class=\"\">inverse problems<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=31&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"13 Publications\" class=\"\">Laplacian eigenfunctions<\/a><\/span> <span style=\"font-size:34px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"82 Publications\" class=\"\">Machine learning<\/a><\/span> <span style=\"font-size:16px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=7&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"40 Publications\" class=\"\">Manifold Learning<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=39&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"6 Publications\" class=\"\">medical imaging<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=15&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"7 Publications\" class=\"\">model reduction<\/a><\/span> <span style=\"font-size:12px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=27&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"29 Publications\" class=\"\">multiscale analysis<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=40&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"5 Publications\" class=\"\">neural networks<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=21&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"20 Publications\" class=\"\">random walks<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=33&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"7 Publications\" class=\"\">reinforcement learning<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=32&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"6 Publications\" class=\"\">representation learning<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=30&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"21 Publications\" class=\"\">spectral graph theory<\/a><\/span> <span style=\"font-size:14px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"34 Publications\" class=\"\">statistics<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=23&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"17 Publications\" class=\"\">stochastic systems<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"10 Publications\" class=\"\">supervised learning<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=2&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"12 Publications\" class=\"\">Unsupervised Learning<\/a><\/span> <span style=\"font-size:11px;\"><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=29&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\" title=\"4 Publications\" class=\"\">wavelets<\/a><\/span> <\/div><div class=\"teachpress_filter\"><select class=\"default\" name=\"yr\" id=\"yr\" tabindex=\"2\" onchange=\"teachpress_jumpMenu('parent',this, 'https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;')\">\r\n                   <option value=\"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=#tppubs\">All years<\/option>\r\n                   <option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2026#tppubs\" >2026<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2025#tppubs\" >2025<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2024#tppubs\" >2024<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2023#tppubs\" >2023<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2022#tppubs\" >2022<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2021#tppubs\" >2021<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2020#tppubs\" >2020<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2019#tppubs\" >2019<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2018#tppubs\" >2018<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2017#tppubs\" >2017<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2016#tppubs\" >2016<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2015#tppubs\" >2015<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2014#tppubs\" >2014<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2013#tppubs\" >2013<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2012#tppubs\" >2012<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2011#tppubs\" >2011<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2010#tppubs\" >2010<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2009#tppubs\" >2009<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2008#tppubs\" >2008<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2007#tppubs\" >2007<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2006#tppubs\" >2006<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2005#tppubs\" >2005<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2004#tppubs\" >2004<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2002#tppubs\" >2002<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=2000#tppubs\" >2000<\/option><option value = \"tgid=&amp;type=&amp;auth=&amp;usr=&amp;yr=0000#tppubs\" >0000<\/option>\r\n                <\/select><select class=\"default\" name=\"type\" id=\"type\" tabindex=\"3\" onchange=\"teachpress_jumpMenu('parent',this, 'https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;')\">\r\n                   <option value=\"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=#tppubs\">All types<\/option>\r\n                   <option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=article#tppubs\" >Journal Articles<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=bachelorthesis#tppubs\" >Bachelor Theses<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=conference#tppubs\" >Conferences<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=inproceedings#tppubs\" >Proceedings Articles<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=journal#tppubs\" >journal<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=misc#tppubs\" >Miscellaneous<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=phdthesis#tppubs\" >PhD Theses<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=proceedings#tppubs\" >Proceedings<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=techreport#tppubs\" >Technical Reports<\/option><option value = \"tgid=&amp;yr=&amp;auth=&amp;usr=&amp;type=unpublished#tppubs\" >Unpublished<\/option>\r\n                <\/select><select class=\"default\" name=\"auth\" id=\"auth\" tabindex=\"5\" onchange=\"teachpress_jumpMenu('parent',this, 'https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;')\">\r\n                   <option value=\"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=#tppubs\">All authors<\/option>\r\n                   <option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=203#tppubs\" > Abramson, Haley G.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=244#tppubs\" > Ahmad, Zan<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=216#tppubs\" > Albert, Christine M.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=245#tppubs\" > Ali, Syed Yusuf<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=183#tppubs\" > Allard, William K<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=47#tppubs\" > Altemose, Nicolas<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=222#tppubs\" > An, Qingci<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=210#tppubs\" > Aronis, Konstantinos N.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=237#tppubs\" > Bayrakta, E<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=185#tppubs\" > Berger, Jim<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=141#tppubs\" > Bongini, Mattia<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=75#tppubs\" > Borghese, N A<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=63#tppubs\" > Bouvrie, Jake<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=144#tppubs\" > Brady, Rachel<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=163#tppubs\" > Bremer, James Jr. C<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=27#tppubs\" > Bridgeford, Eric W<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=232#tppubs\" > Brody, Ryan<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=192#tppubs\" > Browne, James<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=129#tppubs\" > Browne, James Tomita Tyler M.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=194#tppubs\" > Burns, Randal<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=184#tppubs\" > Cassidy, Ryan J<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=106#tppubs\" > Causevic, E<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=231#tppubs\" > Charon, Nicolas<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=60#tppubs\" > Chen, Guangliang<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=151#tppubs\" > Chin, Peter S<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=186#tppubs\" > Chui, Charles K<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=130#tppubs\" > Chung, Jaewon<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=176#tppubs\" > Clementi, Cecilia<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=157#tppubs\" > Coifman, Ronald R<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=213#tppubs\" > Cook, Nancy R.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=179#tppubs\" > Coppi, Andreas C<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=135#tppubs\" > Crosskey, Miles C<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=187#tppubs\" > Czaja, Wojciech<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=140#tppubs\" > Daubechies, Ingrid<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=211#tppubs\" > David Ouyang,<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=177#tppubs\" > Davis, Gus L<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=89#tppubs\" > DeVerse, R A<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=169#tppubs\" > Drineas, Petros<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=175#tppubs\" > Escande, Paul<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=132#tppubs\" > Falk, Benjamin<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=124#tppubs\" > Febbo, P<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=195#tppubs\" >Mauro Maggioni Fei Lu, Sui Tang<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=218#tppubs\" > Feng, Jinchao<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=170#tppubs\" > Ferguson, Kim<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=74#tppubs\" > Ferrari, S<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=142#tppubs\" > Fornasier, Massimo<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=252#tppubs\" >Z. Ahmad G. A. Kevrekidis, M. Maggioni<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=64#tppubs\" > Gerber, S<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=44#tppubs\" > Gerber, Sam<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=178#tppubs\" > Geshwind, Frank B<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=180#tppubs\" > Goetzmann, William<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=123#tppubs\" > Guinney, J<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=143#tppubs\" > Hansen, M<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=139#tppubs\" > Honig, Elisabeth<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=107#tppubs\" > Isenhart, R<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=152#tppubs\" > Iwen, Mark A<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=108#tppubs\" > Jacquin, A<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=109#tppubs\" > John, E R<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=158#tppubs\" > Jones, Peter W<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=122#tppubs\" > Jung, Y -M<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=215#tppubs\" > Kadish, Alan<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=159#tppubs\" > Katz, Nets H<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=103#tppubs\" > Keller, Y<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=166#tppubs\" > Kevrekidis, Ioannis G<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=223#tppubs\" > Kevrekidis, Yannis<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=160#tppubs\" > Krop, Elliot<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=224#tppubs\" > Kuemmerle, Christian<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=95#tppubs\" > Lafon, S<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=161#tppubs\" > Lafon, Stephane<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=206#tppubs\" > Lai, Changxin<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=248#tppubs\" > Lal, Yash<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=255#tppubs\" > Lang, Quanjun<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=234#tppubs\" > Lang, Quanjun<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=190#tppubs\" > Lanteri, Alessandro<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=96#tppubs\" > Lee, A B<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=162#tppubs\" > Lee, Ann B<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=214#tppubs\" > Lee, Daniel C.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=70#tppubs\" > Lee, J<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=84#tppubs\" > Levinson, R<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=10#tppubs\" > Li, Zhongyang<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=148#tppubs\" > Liao, Wenjing<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=65#tppubs\" > Little, Anna V<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=243#tppubs\" > Loeffler, Shane E.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=238#tppubs\" > Lu, F<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=9#tppubs\" > Lu, Fei<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=227#tppubs\" > Lu, Lu<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=257#tppubs\" > Lu, Fei<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=2#tppubs\" > Maggioni, M<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=258#tppubs\" > Maggioni, Mauro<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=7#tppubs\" > Maggioni, Mauro<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=149#tppubs\" > Maggioni, Mauro Y. Wang<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=167#tppubs\" > Mahadevan, Sridhar<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=168#tppubs\" > Mahoney, Michael W<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=219#tppubs\" > Martin, Patrick<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=201#tppubs\" >Jason Miller Mauro Maggioni, Hongda Qiu<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=173#tppubs\" > Mhaskar, Hrushikesh<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=48#tppubs\" > Miga, Karen H<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=128#tppubs\" > Miller, Jason<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=45#tppubs\" > Minsker, Stanislav<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=138#tppubs\" > Monson, Eric<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=212#tppubs\" > Moorthy, M. Vinayaga<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=125#tppubs\" > Mukherjee, S<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=13#tppubs\" > Murphy, James M<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=97#tppubs\" > Nadler, B<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=174#tppubs\" > Nadler, Boaz<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=189#tppubs\" > Okada, David Jason Miller; Jonathan Chrispin; Adityo Prakosa; Natalia Trayanova; Steven Jones; Mauro Maggioni; Katherine Wu R ; C David R.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=171#tppubs\" > Osentoski, Sarah<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=131#tppubs\" > Patsolic, Jesse L<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=204#tppubs\" > Popescu, Dan M.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=110#tppubs\" > Prichep, L S<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=29#tppubs\" > Priebe, Carey E<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=133#tppubs\" > Priebe, Carey E Yim Jason<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=134#tppubs\" > RandalMaggioni, Mauro Burns<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=154#tppubs\" > Rejaie, Reza<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=85#tppubs\" > Rimm, D<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=72#tppubs\" > Rohrdanz, M A<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=66#tppubs\" > Rosasco, Lorenzo<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=259#tppubs\" > S. Yang, M. Maggioni<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=172#tppubs\" > Schul, Raanan<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=207#tppubs\" > Shade, Julie K.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=30#tppubs\" > Shen, Cencheng<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=46#tppubs\" > Strawn, Nate<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=101#tppubs\" > Szlam, A D<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=164#tppubs\" > Szlam, Arthur D<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=11#tppubs\" > Tang, Sui<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=32#tppubs\" > Tomita, Tyler M<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=146#tppubs\" > Tomita, Tyler<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=155#tppubs\" > Torkjazi, M<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=209#tppubs\" > Trayanova, Natalia A.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=233#tppubs\" > Trayanova, Natalia<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=156#tppubs\" > Valafar, M<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=25#tppubs\" > Vigogna, S<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=191#tppubs\" > Vigogna, Stefano<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=26#tppubs\" > Vogelstein, Joshua T<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=181#tppubs\" > Walden, Johan<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=28#tppubs\" > Wang, Qing<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=256#tppubs\" > Wang, Xiong<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=235#tppubs\" > Wang, Xiong<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=145#tppubs\" > Wang, Yang<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=86#tppubs\" > Warner, F J<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=182#tppubs\" > Warner, Frederick<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=188#tppubs\" > Weiss, Guido<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=49#tppubs\" > Willard, Huntington F<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=153#tppubs\" > Willinger, Walter<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=208#tppubs\" > Wu, Katherine C.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=239#tppubs\" > Wu, R<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=242#tppubs\" > Wu, Yantao<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=246#tppubs\" > Yamamoto, Carolyna<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=240#tppubs\" > Yang, S<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=229#tppubs\" > Yang, Sichen<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=228#tppubs\" > Ye, Felix X. -F.<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=247#tppubs\" > Yee, Alana<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=193#tppubs\" > Yim, Jason<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=226#tppubs\" > Yin, Minglang<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=137#tppubs\" > Yin, Rachel<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=205#tppubs\" > Yu, Rebecca<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=251#tppubs\" >S. Chen Z. Ahmad, M. Yin<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=12#tppubs\" > Zhang, Cheng<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=71#tppubs\" > Zheng, W<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=15#tppubs\" > Zhong, Ming<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=250#tppubs\" > Zhou, Jin<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=99#tppubs\" > Zucker, S W<\/option><option value = \"tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=165#tppubs\" > Zucker, Steven W<\/option>\r\n                <\/select><\/div><\/form><div class=\"tablenav\"><div class=\"tablenav-pages\"><span class=\"displaying-num\">115 entries<\/span> <a class=\"page-numbers button disabled\">&laquo;<\/a> <a class=\"page-numbers button disabled\">&lsaquo;<\/a> 1 of 3 <a href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;limit=2&amp;tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=&amp;tsr=#tppubs\" title=\"next page\" class=\"page-numbers button\">&rsaquo;<\/a> <a href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;limit=3&amp;tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=&amp;tsr=#tppubs\" title=\"last page\" class=\"page-numbers button\">&raquo;<\/a> <\/div><\/div><div class=\"teachpress_publication_list\"><h3 class=\"tp_h3\" id=\"tp_h3_2026\">2026<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> S. Yang, M. Maggioni<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1359','tp_links')\" style=\"cursor:pointer;\">Multi-level meta-reinforcement learning with skill-based curriculum<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <span class=\"tp_pub_label_status forthcoming\">Forthcoming<\/span><\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">arXiv, <\/span>Forthcoming.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1359\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1359','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1359\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1359','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1359\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1359','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=33#tppubs\" title=\"Show all publications which have a relationship to this tag\">reinforcement learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=41#tppubs\" title=\"Show all publications which have a relationship to this tag\">transfer learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1359\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{yang2026multilevelmetareinforcementlearningskillbased,<br \/>\r\ntitle = {Multi-level meta-reinforcement learning with skill-based curriculum},<br \/>\r\nauthor = {S. Yang, M. Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2603.08773},<br \/>\r\ndoi = {https:\/\/doi.org\/10.48550\/arXiv.2603.08773},<br \/>\r\nyear  = {2026},<br \/>\r\ndate = {2026-03-09},<br \/>\r\njournal = {arXiv},<br \/>\r\nabstract = {We consider problems in sequential decision making with natural multi-level structure, where sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure has remained a longstanding challenge; we describe an efficient multi-level procedure for repeatedly compressing Markov decision processes (MDPs), wherein a parametric family of policies at one level is treated as single actions in the compressed MDPs at higher levels, while preserving the semantic meanings and structure of the original MDP, and mimicking the natural logic to address a complex MDP. Higher-level MDPs are themselves independent MDPs with less stochasticity, and may be solved using existing algorithms. As a byproduct, spatial or temporal scales may be coarsened at higher levels, making it more efficient to find long-term optimal policies. The multi-level representation delivered by this procedure decouples sub-tasks from each other and usually greatly reduces unnecessary stochasticity and the policy search space, leading to fewer iterations and computations when solving the MDPs. A second fundamental aspect of this work is that these multi-level decompositions plus the factorization of policies into embeddings (problem-specific) and skills (including higher-order functions) yield new transfer opportunities of skills across different problems and different levels. This whole process is framed within curriculum learning, wherein a teacher organizes the student agent&#039;s learning process in a way that gradually increases the difficulty of tasks and and promotes transfer across MDPs and levels within and across curricula. The consistency of this framework and its benefits can be guaranteed under mild assumptions. We demonstrate abstraction, transferability, and curriculum learning in examples, including MazeBase+, a more complex variant of the MazeBase example.},<br \/>\r\nkeywords = {Machine learning, reinforcement learning, transfer learning},<br \/>\r\npubstate = {forthcoming},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1359','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1359\" style=\"display:none;\"><div class=\"tp_abstract_entry\">We consider problems in sequential decision making with natural multi-level structure, where sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure has remained a longstanding challenge; we describe an efficient multi-level procedure for repeatedly compressing Markov decision processes (MDPs), wherein a parametric family of policies at one level is treated as single actions in the compressed MDPs at higher levels, while preserving the semantic meanings and structure of the original MDP, and mimicking the natural logic to address a complex MDP. Higher-level MDPs are themselves independent MDPs with less stochasticity, and may be solved using existing algorithms. As a byproduct, spatial or temporal scales may be coarsened at higher levels, making it more efficient to find long-term optimal policies. The multi-level representation delivered by this procedure decouples sub-tasks from each other and usually greatly reduces unnecessary stochasticity and the policy search space, leading to fewer iterations and computations when solving the MDPs. A second fundamental aspect of this work is that these multi-level decompositions plus the factorization of policies into embeddings (problem-specific) and skills (including higher-order functions) yield new transfer opportunities of skills across different problems and different levels. This whole process is framed within curriculum learning, wherein a teacher organizes the student agent&#039;s learning process in a way that gradually increases the difficulty of tasks and and promotes transfer across MDPs and levels within and across curricula. The consistency of this framework and its benefits can be guaranteed under mild assumptions. We demonstrate abstraction, transferability, and curriculum learning in examples, including MazeBase+, a more complex variant of the MazeBase example.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1359','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1359\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2603.08773\" title=\"https:\/\/arxiv.org\/abs\/2603.08773\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2603.08773<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.48550\/arXiv.2603.08773\" title=\"Follow DOI:https:\/\/doi.org\/10.48550\/arXiv.2603.08773\" target=\"_blank\">doi:https:\/\/doi.org\/10.48550\/arXiv.2603.08773<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1359','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_unpublished\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Lang, Quanjun;  Wang, Xiong;  Lu, Fei;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1358','tp_links')\" style=\"cursor:pointer;\">Learning multi-type heterogeneous interacting particle systems<\/a> <span class=\"tp_pub_type tp_  unpublished\">Unpublished<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_year\">2026<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1358\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1358','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1358\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1358','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1358\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1358','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=58#tppubs\" title=\"Show all publications which have a relationship to this tag\">Artificial Intelligence<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=48#tppubs\" title=\"Show all publications which have a relationship to this tag\">dynamical systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=23#tppubs\" title=\"Show all publications which have a relationship to this tag\">stochastic systems<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1358\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@unpublished{nokey,<br \/>\r\ntitle = {Learning multi-type heterogeneous interacting particle systems},<br \/>\r\nauthor = {Lang, Quanjun and Wang, Xiong and Lu, Fei and Maggioni, Mauro},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2602.03954},<br \/>\r\ndoi = {https:\/\/doi.org\/10.48550\/arXiv.2602.03954},<br \/>\r\nyear  = {2026},<br \/>\r\ndate = {2026-02-05},<br \/>\r\nurldate = {2026-02-05},<br \/>\r\nabstract = {We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging non-convex mixed-integer optimization problem, which we address through a novel three-stage approach. First, we leverage shared structure across agent interactions to recover a low-rank embedding of the system parameters via matrix sensing. Second, we identify discrete interaction types by clustering within the learned embedding. Third, we recover the network weight matrix and kernel coefficients through matrix factorization and a post-processing refinement. We provide theoretical guarantees with estimation error bounds under a Restricted Isometry Property (RIP) assumption and establish conditions for the exact recovery of interaction types based on cluster separability. Numerical experiments on synthetic datasets, including heterogeneous predator-prey systems, demonstrate that our method yields an accurate reconstruction of the underlying dynamics and is robust to noise.},<br \/>\r\nkeywords = {agent-based models, Artificial Intelligence, dynamical systems, interacting particle systems, inverse problems, Machine learning, stochastic systems},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {unpublished}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1358','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1358\" style=\"display:none;\"><div class=\"tp_abstract_entry\">We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging non-convex mixed-integer optimization problem, which we address through a novel three-stage approach. First, we leverage shared structure across agent interactions to recover a low-rank embedding of the system parameters via matrix sensing. Second, we identify discrete interaction types by clustering within the learned embedding. Third, we recover the network weight matrix and kernel coefficients through matrix factorization and a post-processing refinement. We provide theoretical guarantees with estimation error bounds under a Restricted Isometry Property (RIP) assumption and establish conditions for the exact recovery of interaction types based on cluster separability. Numerical experiments on synthetic datasets, including heterogeneous predator-prey systems, demonstrate that our method yields an accurate reconstruction of the underlying dynamics and is robust to noise.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1358','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1358\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2602.03954\" title=\"https:\/\/arxiv.org\/abs\/2602.03954\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2602.03954<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.48550\/arXiv.2602.03954\" title=\"Follow DOI:https:\/\/doi.org\/10.48550\/arXiv.2602.03954\" target=\"_blank\">doi:https:\/\/doi.org\/10.48550\/arXiv.2602.03954<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1358','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2025\">2025<\/h3><div class=\"tp_publication tp_publication_conference\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\">S. Chen Z. Ahmad, M. Yin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1356','tp_links')\" style=\"cursor:pointer;\">Diffeomorphic Latent Neural Operators for Data-Efficient Learning of Solutions to Partial Differential Equations<\/a> <span class=\"tp_pub_type tp_  conference\">Conference<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_booktitle\">Proc. \r\n4th Annual AAAI Workshop on AI to Accelerate Science and Engineering (AI2ASE), <\/span><span class=\"tp_pub_additional_year\">2025<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1356\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1356','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1356\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1356','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=58#tppubs\" title=\"Show all publications which have a relationship to this tag\">Artificial Intelligence<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=53#tppubs\" title=\"Show all publications which have a relationship to this tag\">computational mathematics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1356\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@conference{nokey,<br \/>\r\ntitle = {Diffeomorphic Latent Neural Operators for Data-Efficient Learning of Solutions to Partial Differential Equations},<br \/>\r\nauthor = {Z. Ahmad, S. Chen, M. Yin, A. Kumar, N. Charon, N. Trayanova, M. Maggioni},<br \/>\r\nurl = {https:\/\/ai-2-ase-2025.github.io\/papers\/41.pdf<br \/>\r\nhttps:\/\/arxiv.org\/abs\/2411.18014},<br \/>\r\nyear  = {2025},<br \/>\r\ndate = {2025-03-31},<br \/>\r\nbooktitle = {Proc. <br \/>\r\n4th Annual AAAI Workshop on AI to Accelerate Science and Engineering (AI2ASE)},<br \/>\r\njournal = {Proc. 4th Annual AAAI Workshop on AI to Accelerate Science and Engineering (AI2ASE)},<br \/>\r\nkeywords = {Artificial Intelligence, computational mathematics, Machine learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {conference}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1356','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1356\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/ai-2-ase-2025.github.io\/papers\/41.pdf\" title=\"https:\/\/ai-2-ase-2025.github.io\/papers\/41.pdf\" target=\"_blank\">https:\/\/ai-2-ase-2025.github.io\/papers\/41.pdf<\/a><\/li><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2411.18014\" title=\"https:\/\/arxiv.org\/abs\/2411.18014\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2411.18014<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1356','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2024\">2024<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Wu, Yantao;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1353','tp_links')\" style=\"cursor:pointer;\">Conditional Regression for the Nonlinear Single-Variable Model<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">arXiv, <\/span><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1353\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1353','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1353\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1353','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=51#tppubs\" title=\"Show all publications which have a relationship to this tag\">regression<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1353\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{nokey,<br \/>\r\ntitle = {Conditional Regression for the Nonlinear Single-Variable Model},<br \/>\r\nauthor = {Yantao Wu and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/doi.org\/10.48550\/arXiv.2411.09686},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-11-14},<br \/>\r\nurldate = {2024-11-14},<br \/>\r\njournal = {arXiv},<br \/>\r\nkeywords = {Machine learning, regression, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1353','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1353\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/doi.org\/10.48550\/arXiv.2411.09686\" title=\"https:\/\/doi.org\/10.48550\/arXiv.2411.09686\" target=\"_blank\">https:\/\/doi.org\/10.48550\/arXiv.2411.09686<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1353','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_conference\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Loeffler, Shane E.;  Ahmad, Zan;  Ali, Syed Yusuf;  Yamamoto, Carolyna;  Popescu, Dan M.;  Yee, Alana;  Lal, Yash;  Trayanova, Natalia;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1352','tp_links')\" style=\"cursor:pointer;\">Graph Fourier Neural Kernels (G-FuNK): Learning Solutions of Nonlinear Diffusive Parametric PDEs on Multiple Domains<\/a> <span class=\"tp_pub_type tp_  conference\">Conference<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1352\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1352','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1352\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1352','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1352\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1352','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=57#tppubs\" title=\"Show all publications which have a relationship to this tag\">digital twins<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=31#tppubs\" title=\"Show all publications which have a relationship to this tag\">Laplacian eigenfunctions<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=40#tppubs\" title=\"Show all publications which have a relationship to this tag\">neural networks<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=54#tppubs\" title=\"Show all publications which have a relationship to this tag\">PDEs<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=55#tppubs\" title=\"Show all publications which have a relationship to this tag\">precision medicine<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1352\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@conference{nokey,<br \/>\r\ntitle = {Graph Fourier Neural Kernels (G-FuNK): Learning Solutions of Nonlinear Diffusive Parametric PDEs on Multiple Domains},<br \/>\r\nauthor = {Shane E. Loeffler and Zan Ahmad and Syed Yusuf Ali and Carolyna Yamamoto and Dan M. Popescu and Alana Yee and Yash Lal and Natalia Trayanova and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/doi.org\/10.48550\/arXiv.2410.04655},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-10-09},<br \/>\r\nurldate = {2024-10-09},<br \/>\r\nabstract = {Predicting time-dependent dynamics of complex systems governed by non-linear partial differential equations (PDEs) with varying parameters and domains is a challenging task motivated by applications across various fields. We introduce a novel family of neural operators based on our Graph Fourier Neural Kernels, designed to learn solution generators for nonlinear PDEs in which the highest-order term is diffusive, across multiple domains and parameters. G-FuNK combines components that are parameter- and domain-adapted with others that are not. The domain-adapted components are constructed using a weighted graph on the discretized domain, where the graph Laplacian approximates the highest-order diffusive term, ensuring boundary condition compliance and capturing the parameter and domain-specific behavior. Meanwhile, the learned components transfer across domains and parameters using our variant Fourier Neural Operators. This approach naturally embeds geometric and directional information, improving generalization to new test domains without need for retraining the network. To handle temporal dynamics, our method incorporates an integrated ODE solver to predict the evolution of the system. Experiments show G-FuNK&#039;s capability to accurately approximate heat, reaction diffusion, and cardiac electrophysiology equations across various geometries and anisotropic diffusivity fields. G-FuNK achieves low relative errors on unseen domains and fiber fields, significantly accelerating predictions compared to traditional finite-element solvers.},<br \/>\r\nkeywords = {digital twins, Laplacian eigenfunctions, neural networks, PDEs, precision medicine},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {conference}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1352','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1352\" style=\"display:none;\"><div class=\"tp_abstract_entry\">Predicting time-dependent dynamics of complex systems governed by non-linear partial differential equations (PDEs) with varying parameters and domains is a challenging task motivated by applications across various fields. We introduce a novel family of neural operators based on our Graph Fourier Neural Kernels, designed to learn solution generators for nonlinear PDEs in which the highest-order term is diffusive, across multiple domains and parameters. G-FuNK combines components that are parameter- and domain-adapted with others that are not. The domain-adapted components are constructed using a weighted graph on the discretized domain, where the graph Laplacian approximates the highest-order diffusive term, ensuring boundary condition compliance and capturing the parameter and domain-specific behavior. Meanwhile, the learned components transfer across domains and parameters using our variant Fourier Neural Operators. This approach naturally embeds geometric and directional information, improving generalization to new test domains without need for retraining the network. To handle temporal dynamics, our method incorporates an integrated ODE solver to predict the evolution of the system. Experiments show G-FuNK&#039;s capability to accurately approximate heat, reaction diffusion, and cardiac electrophysiology equations across various geometries and anisotropic diffusivity fields. G-FuNK achieves low relative errors on unseen domains and fiber fields, significantly accelerating predictions compared to traditional finite-element solvers.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1352','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1352\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/doi.org\/10.48550\/arXiv.2410.04655\" title=\"https:\/\/doi.org\/10.48550\/arXiv.2410.04655\" target=\"_blank\">https:\/\/doi.org\/10.48550\/arXiv.2410.04655<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1352','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Kuemmerle, Christian;  Maggioni, Mauro;  Tang, Sui<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1347','tp_links')\" style=\"cursor:pointer;\">Learning Transition Operators From Sparse Space-Time Samples<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">IEEE Transactions on Information Theory, <\/span><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1347\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1347','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1347\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1347','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1347\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1347','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=48#tppubs\" title=\"Show all publications which have a relationship to this tag\">dynamical systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=44#tppubs\" title=\"Show all publications which have a relationship to this tag\">optimization<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=12#tppubs\" title=\"Show all publications which have a relationship to this tag\">sparsity<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1347\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{LearningTransitionOperators_1,<br \/>\r\ntitle = {Learning Transition Operators From Sparse Space-Time Samples},<br \/>\r\nauthor = {Christian Kuemmerle and Mauro Maggioni and Sui Tang},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2212.00746<br \/>\r\nhttps:\/\/ieeexplore.ieee.org\/document\/10558780},<br \/>\r\ndoi = {10.1109\/TIT.2024.3413534},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-06-14},<br \/>\r\nurldate = {2024-06-14},<br \/>\r\njournal = {IEEE Transactions on Information Theory},<br \/>\r\nabstract = {We consider the nonlinear inverse problem of learning a transition operator A from partial observations at different times, in particular from sparse observations of entries of its powers A,A2,\u22ef,AT. This Spatio-Temporal Transition Operator Recovery problem is motivated by the recent interest in learning time-varying graph signals that are driven by graph operators depending on the underlying graph topology. We address the nonlinearity of the problem by embedding it into a higher-dimensional space of suitable block-Hankel matrices, where it becomes a low-rank matrix completion problem, even if A is of full rank. For both a uniform and an adaptive random space-time sampling model, we quantify the recoverability of the transition operator via suitable measures of incoherence of these block-Hankel embedding matrices. For graph transition operators these measures of incoherence depend on the interplay between the dynamics and the graph topology. We develop a suitable non-convex iterative reweighted least squares (IRLS) algorithm, establish its quadratic local convergence, and show that, in optimal scenarios, no more than \ue23b(rnlog(nT)) space-time samples are sufficient to ensure accurate recovery of a rank-r operator A of size n\u00d7n. This establishes that spatial samples can be substituted by a comparable number of space-time samples. We provide an efficient implementation of the proposed IRLS algorithm with space complexity of order O(rnT) and per-iteration time complexity linear in n. Numerical experiments for transition operators based on several graph models confirm that the theoretical findings accurately track empirical phase transitions, and illustrate the applicability and scalability of the proposed algorithm.},<br \/>\r\nkeywords = {dynamical systems, Machine learning, optimization, sparsity, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1347','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1347\" style=\"display:none;\"><div class=\"tp_abstract_entry\">We consider the nonlinear inverse problem of learning a transition operator A from partial observations at different times, in particular from sparse observations of entries of its powers A,A2,\u22ef,AT. This Spatio-Temporal Transition Operator Recovery problem is motivated by the recent interest in learning time-varying graph signals that are driven by graph operators depending on the underlying graph topology. We address the nonlinearity of the problem by embedding it into a higher-dimensional space of suitable block-Hankel matrices, where it becomes a low-rank matrix completion problem, even if A is of full rank. For both a uniform and an adaptive random space-time sampling model, we quantify the recoverability of the transition operator via suitable measures of incoherence of these block-Hankel embedding matrices. For graph transition operators these measures of incoherence depend on the interplay between the dynamics and the graph topology. We develop a suitable non-convex iterative reweighted least squares (IRLS) algorithm, establish its quadratic local convergence, and show that, in optimal scenarios, no more than \ue23b(rnlog(nT)) space-time samples are sufficient to ensure accurate recovery of a rank-r operator A of size n\u00d7n. This establishes that spatial samples can be substituted by a comparable number of space-time samples. We provide an efficient implementation of the proposed IRLS algorithm with space complexity of order O(rnT) and per-iteration time complexity linear in n. Numerical experiments for transition operators based on several graph models confirm that the theoretical findings accurately track empirical phase transitions, and illustrate the applicability and scalability of the proposed algorithm.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1347','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1347\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2212.00746\" title=\"https:\/\/arxiv.org\/abs\/2212.00746\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2212.00746<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/ieeexplore.ieee.org\/document\/10558780\" title=\"https:\/\/ieeexplore.ieee.org\/document\/10558780\" target=\"_blank\">https:\/\/ieeexplore.ieee.org\/document\/10558780<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1109\/TIT.2024.3413534\" title=\"Follow DOI:10.1109\/TIT.2024.3413534\" target=\"_blank\">doi:10.1109\/TIT.2024.3413534<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1347','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Bayrakta, E;  Lu, F;  Maggioni, M;  Wu, R;  Yang, S<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1351','tp_links')\" style=\"cursor:pointer;\">Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <span class=\"tp_pub_label_status forthcoming\">Forthcoming<\/span><\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Bernoulli, <\/span>Forthcoming.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1351\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1351','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1351\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1351','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1351\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{PCAlocaltransitionmatrices,<br \/>\r\ntitle = {Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference},<br \/>\r\nauthor = {E Bayrakta and F Lu and M Maggioni and R Wu and S Yang<br \/>\r\n},<br \/>\r\nurl = {https:\/\/arxiv.org\/html\/2405.02928v2},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-05-03},<br \/>\r\nurldate = {2024-05-03},<br \/>\r\njournal = {Bernoulli},<br \/>\r\nkeywords = {inverse problems, Machine learning, statistics},<br \/>\r\npubstate = {forthcoming},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1351','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1351\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/html\/2405.02928v2\" title=\"https:\/\/arxiv.org\/html\/2405.02928v2\" target=\"_blank\">https:\/\/arxiv.org\/html\/2405.02928v2<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1351','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Yin, Minglang;  Charon, Nicolas;  Brody, Ryan;  Lu, Lu;  Trayanova, Natalia;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1349','tp_links')\" style=\"cursor:pointer;\">A scalable framework for learning the geometry-dependent solution operators of partial differential equations<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Nature Computational Science, <\/span><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1349\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1349','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1349\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1349','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1349\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1349','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=57#tppubs\" title=\"Show all publications which have a relationship to this tag\">digital twins<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=15#tppubs\" title=\"Show all publications which have a relationship to this tag\">model reduction<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=40#tppubs\" title=\"Show all publications which have a relationship to this tag\">neural networks<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=54#tppubs\" title=\"Show all publications which have a relationship to this tag\">PDEs<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=55#tppubs\" title=\"Show all publications which have a relationship to this tag\">precision medicine<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1349\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{DIMON2024,<br \/>\r\ntitle = {A scalable framework for learning the geometry-dependent solution operators of partial differential equations},<br \/>\r\nauthor = {Minglang Yin and Nicolas Charon and Ryan Brody and Lu Lu and Natalia Trayanova and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/pdf\/2402.07250.pdf<br \/>\r\nhttps:\/\/www.nature.com\/articles\/s43588-024-00732-2<br \/>\r\nhttps:\/\/rdcu.be\/d2UPp<br \/>\r\nhttps:\/\/github.com\/MinglangYin\/DIMON},<br \/>\r\ndoi = {10.1038\/s43588-024-00732-2},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-02-13},<br \/>\r\nurldate = {2024-02-13},<br \/>\r\njournal = {Nature Computational Science},<br \/>\r\nabstract = {The solution of a PDE over varying initial\/boundary conditions on multiple domains is needed in a wide variety of applications, but it is computationally expensive if the solution is computed de novo whenever the initial\/boundary conditions of the domain change. We introduce a general operator learning framework, called DIffeomorphic Mapping Operator learNing (DIMON) to learn approximate PDE solutions over a family of domains ${Omega_{theta}}_theta$, that learns the map from initial\/boundary conditions and domain $Omega_theta$ to the solution of the PDE, or to specified functionals thereof. DIMON is based on transporting a given problem (initial\/boundary conditions and domain $Omega_theta$) to a problem on a reference domain $Omega_0$, where training data from multiple problems is used to learn the map to the solution on $Omega_0$, which is then re-mapped to the original domain $Omega_theta$. We consider several problems to demonstrate the performance of the framework in learning both static and time-dependent PDEs on non-rigid geometries; these include solving the Laplace equation, reaction-diffusion equations, and a multiscale PDE that characterizes the electrical propagation on the left ventricle. This work paves the way toward the fast prediction of PDE solutions on a family of domains and the application of neural operators in engineering and precision medicine.},<br \/>\r\nkeywords = {digital twins, Machine learning, model reduction, neural networks, PDEs, precision medicine},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1349','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1349\" style=\"display:none;\"><div class=\"tp_abstract_entry\">The solution of a PDE over varying initial\/boundary conditions on multiple domains is needed in a wide variety of applications, but it is computationally expensive if the solution is computed de novo whenever the initial\/boundary conditions of the domain change. We introduce a general operator learning framework, called DIffeomorphic Mapping Operator learNing (DIMON) to learn approximate PDE solutions over a family of domains ${Omega_{theta}}_theta$, that learns the map from initial\/boundary conditions and domain $Omega_theta$ to the solution of the PDE, or to specified functionals thereof. DIMON is based on transporting a given problem (initial\/boundary conditions and domain $Omega_theta$) to a problem on a reference domain $Omega_0$, where training data from multiple problems is used to learn the map to the solution on $Omega_0$, which is then re-mapped to the original domain $Omega_theta$. We consider several problems to demonstrate the performance of the framework in learning both static and time-dependent PDEs on non-rigid geometries; these include solving the Laplace equation, reaction-diffusion equations, and a multiscale PDE that characterizes the electrical propagation on the left ventricle. This work paves the way toward the fast prediction of PDE solutions on a family of domains and the application of neural operators in engineering and precision medicine.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1349','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1349\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/pdf\/2402.07250.pdf\" title=\"https:\/\/arxiv.org\/pdf\/2402.07250.pdf\" target=\"_blank\">https:\/\/arxiv.org\/pdf\/2402.07250.pdf<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.nature.com\/articles\/s43588-024-00732-2\" title=\"https:\/\/www.nature.com\/articles\/s43588-024-00732-2\" target=\"_blank\">https:\/\/www.nature.com\/articles\/s43588-024-00732-2<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/rdcu.be\/d2UPp\" title=\"https:\/\/rdcu.be\/d2UPp\" target=\"_blank\">https:\/\/rdcu.be\/d2UPp<\/a><\/li><li><i class=\"fab fa-github\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/github.com\/MinglangYin\/DIMON\" title=\"https:\/\/github.com\/MinglangYin\/DIMON\" target=\"_blank\">https:\/\/github.com\/MinglangYin\/DIMON<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1038\/s43588-024-00732-2\" title=\"Follow DOI:10.1038\/s43588-024-00732-2\" target=\"_blank\">doi:10.1038\/s43588-024-00732-2<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1349','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_bachelorthesis\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Lang, Quanjun;  Wang, Xiong;  Lu, Fei;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1350','tp_links')\" style=\"cursor:pointer;\">Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel<\/a> <span class=\"tp_pub_type tp_  bachelorthesis\">Bachelor Thesis<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1350\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1350','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1350\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1350','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=44#tppubs\" title=\"Show all publications which have a relationship to this tag\">optimization<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=23#tppubs\" title=\"Show all publications which have a relationship to this tag\">stochastic systems<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1350\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@bachelorthesis{nokey,<br \/>\r\ntitle = {Interacting Particle Systems on Networks: joint inference of the network and the interaction kernel},<br \/>\r\nauthor = {Quanjun Lang and Xiong Wang and Fei Lu and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/pdf\/2402.08412.pdf},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-02-13},<br \/>\r\njournal = {arXiv},<br \/>\r\nkeywords = {interacting particle systems, Machine learning, optimization, statistics, stochastic systems},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {bachelorthesis}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1350','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1350\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/pdf\/2402.08412.pdf\" title=\"https:\/\/arxiv.org\/pdf\/2402.08412.pdf\" target=\"_blank\">https:\/\/arxiv.org\/pdf\/2402.08412.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1350','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2023\">2023<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Ye, Felix X. -F.;  Yang, Sichen;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1340','tp_links')\" style=\"cursor:pointer;\">Nonlinear model reduction for slow-fast stochastic systems near manifolds<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">J Nonlinear Sci, <\/span><span class=\"tp_pub_additional_volume\">vol. 34, <\/span><span class=\"tp_pub_additional_issue\">iss. 1, <\/span><span class=\"tp_pub_additional_number\">no. 22, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1340\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1340','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1340\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1340','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1340\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1340','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=7#tppubs\" title=\"Show all publications which have a relationship to this tag\">Manifold Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=21#tppubs\" title=\"Show all publications which have a relationship to this tag\">random walks<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=2#tppubs\" title=\"Show all publications which have a relationship to this tag\">Unsupervised Learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1340\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{YYM:ATLAS2,<br \/>\r\ntitle = {Nonlinear model reduction for slow-fast stochastic systems near manifolds},<br \/>\r\nauthor = {Felix X.-F. Ye and Sichen Yang and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2104.02120v1},<br \/>\r\ndoi = {https:\/\/doi.org\/10.1007\/s43670-023-00055-9},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-06-13},<br \/>\r\nurldate = {2023-11-04},<br \/>\r\njournal = {J Nonlinear Sci},<br \/>\r\nvolume = {34},<br \/>\r\nnumber = {22},<br \/>\r\nissue = {1},<br \/>\r\nabstract = {We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only access to a black box simulator from which short bursts of simulation can be obtained, we estimate the invariant manifold, a process of the effective (stochastic) dynamics on it, and construct an efficient simulator thereof. These estimation steps can be performed on-the-fly, leading to efficient exploration of the effective state space, without losing consistency with the underlying dynamics. This construction enables fast and efficient simulation of paths of the effective dynamics, together with estimation of crucial features and observables of such dynamics, including the stationary distribution, identification of metastable states, and residence times and transition rates between them.},<br \/>\r\nkeywords = {inverse problems, Machine learning, Manifold Learning, random walks, statistics, Unsupervised Learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1340','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1340\" style=\"display:none;\"><div class=\"tp_abstract_entry\">We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only access to a black box simulator from which short bursts of simulation can be obtained, we estimate the invariant manifold, a process of the effective (stochastic) dynamics on it, and construct an efficient simulator thereof. These estimation steps can be performed on-the-fly, leading to efficient exploration of the effective state space, without losing consistency with the underlying dynamics. This construction enables fast and efficient simulation of paths of the effective dynamics, together with estimation of crucial features and observables of such dynamics, including the stationary distribution, identification of metastable states, and residence times and transition rates between them.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1340','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1340\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2104.02120v1\" title=\"https:\/\/arxiv.org\/abs\/2104.02120v1\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2104.02120v1<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.1007\/s43670-023-00055-9\" title=\"Follow DOI:https:\/\/doi.org\/10.1007\/s43670-023-00055-9\" target=\"_blank\">doi:https:\/\/doi.org\/10.1007\/s43670-023-00055-9<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1340','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Miller, Jason;  Tang, Sui;  Zhong, Ming;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1337','tp_links')\" style=\"cursor:pointer;\">Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\"> Sampling Theory, Signal Processing, and Data Analysis , <\/span><span class=\"tp_pub_additional_volume\">vol. 21, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1337\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1337','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1337\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1337','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1337\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{LearningInteractionkernels2ndorder,<br \/>\r\ntitle = {Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems},<br \/>\r\nauthor = {Jason Miller and Sui Tang and Ming Zhong and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2010.03729},<br \/>\r\ndoi = {https:\/\/doi.org\/10.1007\/s43670-023-00055-9},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-04-12},<br \/>\r\nurldate = {2023-04-12},<br \/>\r\njournal = { Sampling Theory, Signal Processing, and Data Analysis },<br \/>\r\nvolume = {21},<br \/>\r\nkeywords = {agent-based models, interacting particle systems, inverse problems, Machine learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1337','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1337\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2010.03729\" title=\"https:\/\/arxiv.org\/abs\/2010.03729\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2010.03729<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.1007\/s43670-023-00055-9\" title=\"Follow DOI:https:\/\/doi.org\/10.1007\/s43670-023-00055-9\" target=\"_blank\">doi:https:\/\/doi.org\/10.1007\/s43670-023-00055-9<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1337','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> An, Qingci;  Kevrekidis, Yannis;  Lu, Fei;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1346','tp_links')\" style=\"cursor:pointer;\">Unsupervised learning of observation functions in state-space models by nonparametric moment methods<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Foundations of Data Science, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1346\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1346','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1346\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1346','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=53#tppubs\" title=\"Show all publications which have a relationship to this tag\">computational mathematics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=47#tppubs\" title=\"Show all publications which have a relationship to this tag\">hidden Markov models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=43#tppubs\" title=\"Show all publications which have a relationship to this tag\">optimal transport<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=51#tppubs\" title=\"Show all publications which have a relationship to this tag\">regression<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=23#tppubs\" title=\"Show all publications which have a relationship to this tag\">stochastic systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=2#tppubs\" title=\"Show all publications which have a relationship to this tag\">Unsupervised Learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1346\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{nokey,<br \/>\r\ntitle = {Unsupervised learning of observation functions in state-space models by nonparametric moment methods},<br \/>\r\nauthor = {Qingci An and Yannis Kevrekidis and Fei Lu and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2207.05242<br \/>\r\nhttps:\/\/doi.org\/10.3934\/fods.2023002},<br \/>\r\ndoi = {10.3934\/fods.2023002},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-02-01},<br \/>\r\nurldate = {2023-02-01},<br \/>\r\njournal = {Foundations of Data Science},<br \/>\r\nkeywords = {computational mathematics, hidden Markov models, inverse problems, Machine learning, optimal transport, regression, statistics, stochastic systems, Unsupervised Learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1346','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1346\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2207.05242\" title=\"https:\/\/arxiv.org\/abs\/2207.05242\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2207.05242<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/doi.org\/10.3934\/fods.2023002\" title=\"https:\/\/doi.org\/10.3934\/fods.2023002\" target=\"_blank\">https:\/\/doi.org\/10.3934\/fods.2023002<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.3934\/fods.2023002\" title=\"Follow DOI:10.3934\/fods.2023002\" target=\"_blank\">doi:10.3934\/fods.2023002<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1346','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2022\">2022<\/h3><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Feng, Jinchao;  Maggioni, Mauro;  Martin, Patrick;  Zhong, Ming<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1345','tp_links')\" style=\"cursor:pointer;\">Learning Interaction Variables and Kernels from Observations of Agent-Based Systems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">IFAC Proceedings, <\/span><span class=\"tp_pub_additional_year\">2022<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1345\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1345','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1345\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1345','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1345\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1345','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1345\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{nokey,<br \/>\r\ntitle = {Learning Interaction Variables and Kernels from Observations of Agent-Based Systems},<br \/>\r\nauthor = {Jinchao Feng and Mauro Maggioni and Patrick Martin and Ming Zhong},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2208.02758<br \/>\r\n},<br \/>\r\ndoi = {https:\/\/doi.org\/10.1016\/j.ifacol.2022.11.046},<br \/>\r\nyear  = {2022},<br \/>\r\ndate = {2022-08-04},<br \/>\r\nurldate = {2022-08-04},<br \/>\r\nbooktitle = {IFAC Proceedings},<br \/>\r\njournal = {arXiV preprint},<br \/>\r\nabstract = {Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of the state of pairs of agents. Yet, these interaction rules can generate self-organized dynamics, with complex emergent behaviors (clustering, flocking, swarming, etc.). We propose a learning technique that, given observations of states and velocities along trajectories of the agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself, in a nonparametric fashion. This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data (states and velocities of all the agents). We demonstrate the learning capability of our method to a variety of first-order interacting systems.},<br \/>\r\nkeywords = {agent-based models, inverse problems, Machine learning, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1345','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1345\" style=\"display:none;\"><div class=\"tp_abstract_entry\">Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc&#8230;), functions of the state of pairs of agents. Yet, these interaction rules can generate self-organized dynamics, with complex emergent behaviors (clustering, flocking, swarming, etc.). We propose a learning technique that, given observations of states and velocities along trajectories of the agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself, in a nonparametric fashion. This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data (states and velocities of all the agents). We demonstrate the learning capability of our method to a variety of first-order interacting systems.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1345','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1345\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2208.02758\" title=\"https:\/\/arxiv.org\/abs\/2208.02758\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2208.02758<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.1016\/j.ifacol.2022.11.046\" title=\"Follow DOI:https:\/\/doi.org\/10.1016\/j.ifacol.2022.11.046\" target=\"_blank\">doi:https:\/\/doi.org\/10.1016\/j.ifacol.2022.11.046<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1345','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_phdthesis\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Zhou, Jin;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1355','tp_links')\" style=\"cursor:pointer;\">Learning Multiscale Approximations of Functions between Manifolds<\/a> <span class=\"tp_pub_type tp_  phdthesis\">PhD Thesis<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_year\">2022<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1355\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1355','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1355\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1355','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1355\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1355','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=49#tppubs\" title=\"Show all publications which have a relationship to this tag\">geometric wavelets<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=7#tppubs\" title=\"Show all publications which have a relationship to this tag\">Manifold Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1355\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@phdthesis{nokey,<br \/>\r\ntitle = {Learning Multiscale Approximations of Functions between Manifolds},<br \/>\r\nauthor = {Jin Zhou and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/jscholarship.library.jhu.edu\/items\/3a61646e-3c03-47a4-9768-180cf67e5fc4\/full},<br \/>\r\nyear  = {2022},<br \/>\r\ndate = {2022-07-18},<br \/>\r\nurldate = {2022-07-18},<br \/>\r\nabstract = {In many machine learning applications, data sets are in a high dimensional space but have a low-dimensional structure. The intrinsic dimension of the structure is often much smaller than the ambient dimension. This has given rise to the studies on manifold learning, when the low-dimensional structure is a manifold, and dictionary learning, when the low-dimensional structure is a set of sparse linear combinations of vectors from a finite dictionary. However, there has been very limited research for transformations between two high dimensional data sets. These transformations can be hard and expensive to store and compute. Furthermore, the existing algorithms are limited to be applied due to the high dimensionality of the two data sets. This thesis considers the problem of estimating a function between two high dimensional data sets. Both the domain and the range are supported on low-dimensional manifolds, given random samples in the domain and corresponding samples in the range perturbed by bounded noise. Geometric Multi-Resolution Analysis (GMRA) constructs low-dimensional geometric multiscale approximations of the data set lying on or near a manifold. We estimate these two unknown manifolds using GMRA and approximate the functions locally by multiscale linear maps. We obtain the optimal learning rate up to a log factor, depending on the intrinsic dimension of data, and circumvent the curse of dimensionality in the domain and the range.},<br \/>\r\nkeywords = {geometric wavelets, Machine learning, Manifold Learning, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {phdthesis}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1355','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1355\" style=\"display:none;\"><div class=\"tp_abstract_entry\">In many machine learning applications, data sets are in a high dimensional space but have a low-dimensional structure. The intrinsic dimension of the structure is often much smaller than the ambient dimension. This has given rise to the studies on manifold learning, when the low-dimensional structure is a manifold, and dictionary learning, when the low-dimensional structure is a set of sparse linear combinations of vectors from a finite dictionary. However, there has been very limited research for transformations between two high dimensional data sets. These transformations can be hard and expensive to store and compute. Furthermore, the existing algorithms are limited to be applied due to the high dimensionality of the two data sets. This thesis considers the problem of estimating a function between two high dimensional data sets. Both the domain and the range are supported on low-dimensional manifolds, given random samples in the domain and corresponding samples in the range perturbed by bounded noise. Geometric Multi-Resolution Analysis (GMRA) constructs low-dimensional geometric multiscale approximations of the data set lying on or near a manifold. We estimate these two unknown manifolds using GMRA and approximate the functions locally by multiscale linear maps. We obtain the optimal learning rate up to a log factor, depending on the intrinsic dimension of data, and circumvent the curse of dimensionality in the domain and the range.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1355','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1355\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/jscholarship.library.jhu.edu\/items\/3a61646e-3c03-47a4-9768-180cf67e5fc4\/full\" title=\"https:\/\/jscholarship.library.jhu.edu\/items\/3a61646e-3c03-47a4-9768-180cf67e5fc4\/[...]\" target=\"_blank\">https:\/\/jscholarship.library.jhu.edu\/items\/3a61646e-3c03-47a4-9768-180cf67e5fc4\/[&#8230;]<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1355','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Popescu, Dan M.;  Shade, Julie K.;  Lai, Changxin;  Aronis, Konstantinos N.;  David Ouyang,;  Moorthy, M. Vinayaga;  Cook, Nancy R.;  Lee, Daniel C.;  Kadish, Alan;  Albert, Christine M.;  Wu, Katherine C.;  Maggioni, Mauro;  Trayanova, Natalia A.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1344','tp_links')\" style=\"cursor:pointer;\">Arrhythmic sudden death survival prediction using deep learning analysis of scarring in the heart<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Nature Cardiovascular Research, <\/span><span class=\"tp_pub_additional_year\">2022<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1344\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1344','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1344\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1344','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=57#tppubs\" title=\"Show all publications which have a relationship to this tag\">digital twins<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=39#tppubs\" title=\"Show all publications which have a relationship to this tag\">medical imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=40#tppubs\" title=\"Show all publications which have a relationship to this tag\">neural networks<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=55#tppubs\" title=\"Show all publications which have a relationship to this tag\">precision medicine<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1344\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{SCDsurvival1,<br \/>\r\ntitle = {Arrhythmic sudden death survival prediction using deep learning analysis of scarring in the heart},<br \/>\r\nauthor = {Dan M. Popescu and Julie K. Shade and Changxin Lai and Konstantinos N. Aronis and David Ouyang, and M. Vinayaga Moorthy and Nancy R. Cook and Daniel C. Lee and Alan Kadish and Christine M. Albert and Katherine C. Wu and Mauro Maggioni and Natalia A. Trayanova<br \/>\r\n},<br \/>\r\nurl = {https:\/\/rdcu.be\/cKSAl},<br \/>\r\ndoi = {10.1038\/s44161-022-00041-9},<br \/>\r\nyear  = {2022},<br \/>\r\ndate = {2022-03-07},<br \/>\r\nurldate = {2022-03-07},<br \/>\r\njournal = {Nature Cardiovascular Research},<br \/>\r\nkeywords = {digital twins, Machine learning, medical imaging, neural networks, precision medicine},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1344','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1344\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/rdcu.be\/cKSAl\" title=\"https:\/\/rdcu.be\/cKSAl\" target=\"_blank\">https:\/\/rdcu.be\/cKSAl<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1038\/s44161-022-00041-9\" title=\"Follow DOI:10.1038\/s44161-022-00041-9\" target=\"_blank\">doi:10.1038\/s44161-022-00041-9<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1344','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Lanteri, Alessandro;  Maggioni, Mauro;  Vigogna, Stefano<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1332','tp_links')\" style=\"cursor:pointer;\">Conditional regression for single-index models<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Bernoulli, <\/span><span class=\"tp_pub_additional_year\">2022<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1332\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1332','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1332\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1332','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=51#tppubs\" title=\"Show all publications which have a relationship to this tag\">regression<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1332\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{aless2020conditional,<br \/>\r\ntitle = {Conditional regression for single-index models},<br \/>\r\nauthor = {Alessandro Lanteri and Mauro Maggioni and Stefano Vigogna},<br \/>\r\nurl = {https:\/\/www.e-publications.org\/ims\/submission\/BEJ\/user\/submissionFile\/49273?confirm=22a655d7<br \/>\r\nhttps:\/\/arxiv.org\/abs\/2002.10008},<br \/>\r\ndoi = {10.3150\/22-BEJ1482},<br \/>\r\nyear  = {2022},<br \/>\r\ndate = {2022-01-01},<br \/>\r\nurldate = {2022-01-01},<br \/>\r\njournal = {Bernoulli},<br \/>\r\nkeywords = {regression, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1332','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1332\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.e-publications.org\/ims\/submission\/BEJ\/user\/submissionFile\/49273?confirm=22a655d7\" title=\"https:\/\/www.e-publications.org\/ims\/submission\/BEJ\/user\/submissionFile\/49273?conf[...]\" target=\"_blank\">https:\/\/www.e-publications.org\/ims\/submission\/BEJ\/user\/submissionFile\/49273?conf[&#8230;]<\/a><\/li><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2002.10008\" title=\"https:\/\/arxiv.org\/abs\/2002.10008\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2002.10008<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.3150\/22-BEJ1482\" title=\"Follow DOI:10.3150\/22-BEJ1482\" target=\"_blank\">doi:10.3150\/22-BEJ1482<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1332','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2021\">2021<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Abramson, Haley G.;  Popescu, Dan M.;  Yu, Rebecca;  Lai, Changxin;  Shade, Julie K.;  Wu, Katherine C.;  Maggioni, Mauro;  Trayanova, Natalia A.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1338','tp_links')\" style=\"cursor:pointer;\">Anatomically-Informed Deep Learning on Contrast-Enhanced Cardiac MRI for Scar Segmentation and Clinical Feature Extraction<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Cardiovascular Digital Health Journal, <\/span><span class=\"tp_pub_additional_year\">2021<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1338\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1338','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1338\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1338','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=57#tppubs\" title=\"Show all publications which have a relationship to this tag\">digital twins<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34#tppubs\" title=\"Show all publications which have a relationship to this tag\">imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=39#tppubs\" title=\"Show all publications which have a relationship to this tag\">medical imaging<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1338\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{AnatLGECMRInn,<br \/>\r\ntitle = {Anatomically-Informed Deep Learning on Contrast-Enhanced Cardiac MRI for Scar Segmentation and Clinical Feature Extraction},<br \/>\r\nauthor = {Haley G. Abramson and Dan M. Popescu and Rebecca Yu and Changxin Lai and Julie K. Shade and Katherine C. Wu and Mauro Maggioni and Natalia A. Trayanova},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2010.11081<br \/>\r\nhttps:\/\/www.cvdigitalhealthjournal.com\/article\/S2666-6936(21)00131-6\/pdf<br \/>\r\nhttps:\/\/www.ahajournals.org\/doi\/abs\/10.1161\/circ.142.suppl_3.16017<br \/>\r\nhttp:\/\/jhu.technologypublisher.com\/technology\/43121},<br \/>\r\ndoi = {https:\/\/doi.org\/10.1016\/j.cvdhj.2021.11.007},<br \/>\r\nyear  = {2021},<br \/>\r\ndate = {2021-11-25},<br \/>\r\nurldate = {2021-11-25},<br \/>\r\njournal = {Cardiovascular Digital Health Journal},<br \/>\r\nkeywords = {digital twins, imaging, Machine learning, medical imaging},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1338','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1338\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2010.11081\" title=\"https:\/\/arxiv.org\/abs\/2010.11081\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2010.11081<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.cvdigitalhealthjournal.com\/article\/S2666-6936(21)00131-6\/pdf\" title=\"https:\/\/www.cvdigitalhealthjournal.com\/article\/S2666-6936(21)00131-6\/pdf\" target=\"_blank\">https:\/\/www.cvdigitalhealthjournal.com\/article\/S2666-6936(21)00131-6\/pdf<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.ahajournals.org\/doi\/abs\/10.1161\/circ.142.suppl_3.16017\" title=\"https:\/\/www.ahajournals.org\/doi\/abs\/10.1161\/circ.142.suppl_3.16017\" target=\"_blank\">https:\/\/www.ahajournals.org\/doi\/abs\/10.1161\/circ.142.suppl_3.16017<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/jhu.technologypublisher.com\/technology\/43121\" title=\"http:\/\/jhu.technologypublisher.com\/technology\/43121\" target=\"_blank\">http:\/\/jhu.technologypublisher.com\/technology\/43121<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.1016\/j.cvdhj.2021.11.007\" title=\"Follow DOI:https:\/\/doi.org\/10.1016\/j.cvdhj.2021.11.007\" target=\"_blank\">doi:https:\/\/doi.org\/10.1016\/j.cvdhj.2021.11.007<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1338','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_unpublished\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Zhong, Ming;  Miller, Jason;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1343','tp_links')\" style=\"cursor:pointer;\">Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemerides<\/a> <span class=\"tp_pub_type tp_  unpublished\">Unpublished<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_year\">2021<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1343\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1343','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1343\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1343','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1343\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@unpublished{zhongEphermerids,<br \/>\r\ntitle = {Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemerides},<br \/>\r\nauthor = {Ming Zhong and Jason Miller and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2108.11894},<br \/>\r\nyear  = {2021},<br \/>\r\ndate = {2021-08-26},<br \/>\r\nurldate = {2021-08-26},<br \/>\r\njournal = {arXiv preprint},<br \/>\r\nkeywords = {agent-based models, interacting particle systems, Machine learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {unpublished}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1343','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1343\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2108.11894\" title=\"https:\/\/arxiv.org\/abs\/2108.11894\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2108.11894<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1343','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Liao, Wenjing;  Maggioni, Mauro;  Vigogna, Stefano<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1261','tp_links')\" style=\"cursor:pointer;\">Multiscale regression on intrinsically low-dimensional sets<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Mathematics in Engineering, <\/span><span class=\"tp_pub_additional_volume\">vol. 4, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_year\">2021<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1261\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1261','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1261\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1261','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=7#tppubs\" title=\"Show all publications which have a relationship to this tag\">Manifold Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1261\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{LiaoMaggioniVigogna:MultiscaleRegressionManifolds,<br \/>\r\ntitle = {Multiscale regression on intrinsically low-dimensional sets},<br \/>\r\nauthor = {Wenjing Liao and Mauro Maggioni and Stefano Vigogna},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2101.05119v1<br \/>\r\nhttp:\/\/www.aimspress.com\/aimspress-data\/mine\/2022\/4\/PDF\/mine-04-04-028.pdf},<br \/>\r\ndoi = {DOI:10.3934\/mine.2022028},<br \/>\r\nyear  = {2021},<br \/>\r\ndate = {2021-08-24},<br \/>\r\nurldate = {2021-08-24},<br \/>\r\njournal = {Mathematics in Engineering},<br \/>\r\nvolume = {4},<br \/>\r\nnumber = {4},<br \/>\r\nkeywords = {Machine learning, Manifold Learning, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1261','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1261\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2101.05119v1\" title=\"https:\/\/arxiv.org\/abs\/2101.05119v1\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2101.05119v1<\/a><\/li><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.aimspress.com\/aimspress-data\/mine\/2022\/4\/PDF\/mine-04-04-028.pdf\" title=\"http:\/\/www.aimspress.com\/aimspress-data\/mine\/2022\/4\/PDF\/mine-04-04-028.pdf\" target=\"_blank\">http:\/\/www.aimspress.com\/aimspress-data\/mine\/2022\/4\/PDF\/mine-04-04-028.pdf<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/DOI:10.3934\/mine.2022028\" title=\"Follow DOI:DOI:10.3934\/mine.2022028\" target=\"_blank\">doi:DOI:10.3934\/mine.2022028<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1261','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Lu, Fei;  Maggioni, Mauro;  Tang, Sui<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1342','tp_links')\" style=\"cursor:pointer;\">Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Foundation of Computational Mathematics, <\/span><span class=\"tp_pub_additional_year\">2021<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1342\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1342','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1342\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1342','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1342\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1342','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=23#tppubs\" title=\"Show all publications which have a relationship to this tag\">stochastic systems<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1342\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{learningStochasticInteracting,<br \/>\r\ntitle = {Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories},<br \/>\r\nauthor = {Fei Lu and Mauro Maggioni and Sui Tang},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2007.15174<br \/>\r\nhttps:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09521-z.pdf},<br \/>\r\ndoi = {doi.org\/10.1007\/s10208-021-09521-z},<br \/>\r\nyear  = {2021},<br \/>\r\ndate = {2021-04-01},<br \/>\r\nurldate = {2021-04-01},<br \/>\r\njournal = {Foundation of Computational Mathematics},<br \/>\r\nabstract = {We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of the positions of the particles, in either continuous or discrete time, along multiple independent trajectories. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator constrained to suitable hypothesis spaces adaptive to data. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator, and that in fact it converges at a near-optimal learning rate, equal to the min-max rate of 1-dimensional non-parametric regression. In particular, this rate is independent of the dimension of the state space, which is typically very high. We also analyze the discretization errors in the case of discrete-time observations, showing that it is of order 1\/2 in terms of the time spacings between observations. This term, when large, dominates the sampling error and the approximation error, preventing convergence of the estimator. Finally, we exhibit an efficient parallel al- gorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.},<br \/>\r\nkeywords = {agent-based models, interacting particle systems, Machine learning, statistics, stochastic systems},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1342','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1342\" style=\"display:none;\"><div class=\"tp_abstract_entry\">We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of the positions of the particles, in either continuous or discrete time, along multiple independent trajectories. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator constrained to suitable hypothesis spaces adaptive to data. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator, and that in fact it converges at a near-optimal learning rate, equal to the min-max rate of 1-dimensional non-parametric regression. In particular, this rate is independent of the dimension of the state space, which is typically very high. We also analyze the discretization errors in the case of discrete-time observations, showing that it is of order 1\/2 in terms of the time spacings between observations. This term, when large, dominates the sampling error and the approximation error, preventing convergence of the estimator. Finally, we exhibit an efficient parallel al- gorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1342','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1342\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2007.15174\" title=\"https:\/\/arxiv.org\/abs\/2007.15174\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2007.15174<\/a><\/li><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09521-z.pdf\" title=\"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09521-z.pdf\" target=\"_blank\">https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09521-z.pdf<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/doi.org\/10.1007\/s10208-021-09521-z\" title=\"Follow DOI:doi.org\/10.1007\/s10208-021-09521-z\" target=\"_blank\">doi:doi.org\/10.1007\/s10208-021-09521-z<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1342','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Lu, Fei;  Li, Zhongyang;  Maggioni, Mauro;  Tang, Sui;  Zhang, Cheng<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1240','tp_links')\" style=\"cursor:pointer;\">On the identifiability of interaction functions in systems of interacting particles<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Stochastic Processes and their Applications, <\/span><span class=\"tp_pub_additional_volume\">vol. 132, <\/span><span class=\"tp_pub_additional_year\">2021<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1240\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1240','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1240\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1240','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=15#tppubs\" title=\"Show all publications which have a relationship to this tag\">model reduction<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1240\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{IdentifiabilityInteractionFunctions,<br \/>\r\ntitle = {On the identifiability of interaction functions in systems of interacting particles},<br \/>\r\nauthor = {Fei Lu and Zhongyang Li and Mauro Maggioni and Sui Tang and Cheng Zhang},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/1912.11965},<br \/>\r\ndoi = {https:\/\/doi.org\/10.1016\/j.spa.2020.10.005},<br \/>\r\nyear  = {2021},<br \/>\r\ndate = {2021-02-01},<br \/>\r\njournal = {Stochastic Processes and their Applications},<br \/>\r\nvolume = {132},<br \/>\r\nkeywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1240','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1240\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/1912.11965\" title=\"https:\/\/arxiv.org\/abs\/1912.11965\" target=\"_blank\">https:\/\/arxiv.org\/abs\/1912.11965<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.1016\/j.spa.2020.10.005\" title=\"Follow DOI:https:\/\/doi.org\/10.1016\/j.spa.2020.10.005\" target=\"_blank\">doi:https:\/\/doi.org\/10.1016\/j.spa.2020.10.005<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1240','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_proceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\">Jason Miller Mauro Maggioni, Hongda Qiu<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1341','tp_links')\" style=\"cursor:pointer;\"> Learning Interaction Kernels for Agent Systems on Riemannian Manifolds<\/a> <span class=\"tp_pub_type tp_  proceedings\">Proceedings<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_howpublished\">ICML, <\/span><span class=\"tp_pub_additional_year\">2021<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1341\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1341','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1341\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1341','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1341\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1341','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=15#tppubs\" title=\"Show all publications which have a relationship to this tag\">model reduction<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1341\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@proceedings{AgentSystemsManifolds,<br \/>\r\ntitle = { Learning Interaction Kernels for Agent Systems on Riemannian Manifolds},<br \/>\r\nauthor = {Mauro Maggioni, Jason Miller, Hongda Qiu, Ming Zhong},<br \/>\r\nurl = {http:\/\/proceedings.mlr.press\/v139\/maggioni21a.html<br \/>\r\nhttps:\/\/icml.cc\/virtual\/2021\/poster\/10167<br \/>\r\nhttps:\/\/arxiv.org\/abs\/2102.00327},<br \/>\r\nyear  = {2021},<br \/>\r\ndate = {2021-01-30},<br \/>\r\nurldate = {2021-01-30},<br \/>\r\nabstract = {Interacting agent and particle systems are extensively used to model complex phenomena in science and engineering. We consider the problem of learning interaction kernels in these dynamical systems constrained to evolve on Riemannian manifolds from given trajectory data. The models we consider are based on interaction kernels depending on pairwise Riemannian distances between agents, with agents interacting locally along the direction of the shortest geodesic connecting them. We show that our estimators converge at a rate that is independent of the dimension of the state space, and derive bounds on the trajectory estimation error, on the manifold, between the observed and estimated dynamics. We demonstrate the performance of our estimator on two classical first order interacting systems: Opinion Dynamics and a Predator-Swarm system, with each system constrained on two prototypical manifolds, the 2-dimensional sphere and the Poincar\u00e9 disk model of hyperbolic space.},<br \/>\r\nhowpublished = {ICML},<br \/>\r\nkeywords = {agent-based models, interacting particle systems, Machine learning, model reduction, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {proceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1341','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1341\" style=\"display:none;\"><div class=\"tp_abstract_entry\">Interacting agent and particle systems are extensively used to model complex phenomena in science and engineering. We consider the problem of learning interaction kernels in these dynamical systems constrained to evolve on Riemannian manifolds from given trajectory data. The models we consider are based on interaction kernels depending on pairwise Riemannian distances between agents, with agents interacting locally along the direction of the shortest geodesic connecting them. We show that our estimators converge at a rate that is independent of the dimension of the state space, and derive bounds on the trajectory estimation error, on the manifold, between the observed and estimated dynamics. We demonstrate the performance of our estimator on two classical first order interacting systems: Opinion Dynamics and a Predator-Swarm system, with each system constrained on two prototypical manifolds, the 2-dimensional sphere and the Poincar\u00e9 disk model of hyperbolic space.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1341','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1341\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/proceedings.mlr.press\/v139\/maggioni21a.html\" title=\"http:\/\/proceedings.mlr.press\/v139\/maggioni21a.html\" target=\"_blank\">http:\/\/proceedings.mlr.press\/v139\/maggioni21a.html<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/icml.cc\/virtual\/2021\/poster\/10167\" title=\"https:\/\/icml.cc\/virtual\/2021\/poster\/10167\" target=\"_blank\">https:\/\/icml.cc\/virtual\/2021\/poster\/10167<\/a><\/li><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2102.00327\" title=\"https:\/\/arxiv.org\/abs\/2102.00327\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2102.00327<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1341','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\">Mauro Maggioni Fei Lu, Sui Tang<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1339','tp_links')\" style=\"cursor:pointer;\">Learning interaction kernels in heterogeneous systems of agents from multiple trajectories<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journ. Mach. Learn. res., <\/span><span class=\"tp_pub_additional_volume\">vol. 2, <\/span><span class=\"tp_pub_additional_number\">no. 32, <\/span><span class=\"tp_pub_additional_pages\">pp. 1\u201367, <\/span><span class=\"tp_pub_additional_year\">2021<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_1339\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1339','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_1339\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1339','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1339\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1339','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=4#tppubs\" title=\"Show all publications which have a relationship to this tag\">Active Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1339\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{LuMMTang21,<br \/>\r\ntitle = {Learning interaction kernels in heterogeneous systems of agents from multiple trajectories},<br \/>\r\nauthor = {Fei Lu, Mauro Maggioni, Sui Tang},<br \/>\r\nurl = {https:\/\/jmlr.csail.mit.edu\/papers\/v22\/19-861.html},<br \/>\r\nyear  = {2021},<br \/>\r\ndate = {2021-01-01},<br \/>\r\njournal = {Journ. Mach. Learn. res.},<br \/>\r\nvolume = {2},<br \/>\r\nnumber = {32},<br \/>\r\npages = {1--67},<br \/>\r\nabstract = {Systems of interacting particles, or agents, have wide applications in many disciplines, including Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from observation data is a fundamental task that can provide meaningful insights and accurate predictions of the behaviour of the agents. In this paper, we consider the inverse problem of learning interaction laws given data from multiple trajectories, in a nonparametric fashion, when the interaction kernels depend on pairwise distances. We establish a condition for learnability of interaction kernels, and construct an estimator based on the minimization of a suitably regularized least squares functional, that is guaranteed to converge, in a suitable L^2 space, at the optimal min-max rate for 1-dimensional nonparametric regression. We propose an efficient learning algorithm to construct such estimator, which can be implemented in parallel for multiple trajectories and is therefore well-suited for the high dimensional, big data regime. Numerical simulations on a variety examples, including opinion dynamics, predator-prey and swarm dynamics and heterogeneous particle dynamics, suggest that the learnability condition is satisfied in models used in practice, and the rate of convergence of our estimator is consistent with the theory. These simulations also suggest that our estimators are robust to noise in the observations, and can produce accurate predictions of trajectories in large time intervals, even when they are learned from observations in short time intervals.},<br \/>\r\nkeywords = {Active Learning, interacting particle systems, inverse problems, Machine learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1339','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_1339\" style=\"display:none;\"><div class=\"tp_abstract_entry\">Systems of interacting particles, or agents, have wide applications in many disciplines, including Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from observation data is a fundamental task that can provide meaningful insights and accurate predictions of the behaviour of the agents. In this paper, we consider the inverse problem of learning interaction laws given data from multiple trajectories, in a nonparametric fashion, when the interaction kernels depend on pairwise distances. We establish a condition for learnability of interaction kernels, and construct an estimator based on the minimization of a suitably regularized least squares functional, that is guaranteed to converge, in a suitable L^2 space, at the optimal min-max rate for 1-dimensional nonparametric regression. We propose an efficient learning algorithm to construct such estimator, which can be implemented in parallel for multiple trajectories and is therefore well-suited for the high dimensional, big data regime. Numerical simulations on a variety examples, including opinion dynamics, predator-prey and swarm dynamics and heterogeneous particle dynamics, suggest that the learnability condition is satisfied in models used in practice, and the rate of convergence of our estimator is consistent with the theory. These simulations also suggest that our estimators are robust to noise in the observations, and can produce accurate predictions of trajectories in large time intervals, even when they are learned from observations in short time intervals.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1339','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1339\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/jmlr.csail.mit.edu\/papers\/v22\/19-861.html\" title=\"https:\/\/jmlr.csail.mit.edu\/papers\/v22\/19-861.html\" target=\"_blank\">https:\/\/jmlr.csail.mit.edu\/papers\/v22\/19-861.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1339','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2020\">2020<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Tomita, Tyler M;  Browne, James;  Shen, Cencheng;  Chung, Jaewon;  Patsolic, Jesse L;  Falk, Benjamin;  Priebe, Carey E;  Yim, Jason;  Burns, Randal;  Maggioni, Mauro;  Vogelstein, Joshua T<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1335','tp_links')\" style=\"cursor:pointer;\">Sparse Projection Oblique Randomer Forests<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of Machine Learning Research, <\/span><span class=\"tp_pub_additional_volume\">vol. 21, <\/span><span class=\"tp_pub_additional_number\">no. 104, <\/span><span class=\"tp_pub_additional_pages\">pp. 1-39, <\/span><span class=\"tp_pub_additional_year\">2020<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1335\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1335','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1335\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1335','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1335\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{SparseObliqueRandomerForestsb,<br \/>\r\ntitle = {Sparse Projection Oblique Randomer Forests},<br \/>\r\nauthor = {Tyler M Tomita and James Browne and Cencheng Shen and Jaewon Chung and Jesse L Patsolic and Benjamin Falk and Carey E Priebe and Jason Yim and Randal Burns and Mauro Maggioni and Joshua T Vogelstein},<br \/>\r\nurl = {http:\/\/jmlr.org\/papers\/v21\/18-664.html},<br \/>\r\nyear  = {2020},<br \/>\r\ndate = {2020-01-01},<br \/>\r\njournal = {Journal of Machine Learning Research},<br \/>\r\nvolume = {21},<br \/>\r\nnumber = {104},<br \/>\r\npages = {1-39},<br \/>\r\nkeywords = {Machine learning, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1335','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1335\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/jmlr.org\/papers\/v21\/18-664.html\" title=\"http:\/\/jmlr.org\/papers\/v21\/18-664.html\" target=\"_blank\">http:\/\/jmlr.org\/papers\/v21\/18-664.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1335','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Okada, David Jason Miller; Jonathan Chrispin; Adityo Prakosa; Natalia Trayanova; Steven Jones; Mauro Maggioni; Katherine Wu R ; C David R.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1238','tp_links')\" style=\"cursor:pointer;\">Substrate Spatial Complexity Analysis for the Prediction of Ventricular Arrhythmias in Patients with Ischemic Cardiomyopathy<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Circulation: Arrhythmia and Electrophysiology, <\/span><span class=\"tp_pub_additional_year\">2020<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1238\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1238','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1238\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1238','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34#tppubs\" title=\"Show all publications which have a relationship to this tag\">imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=31#tppubs\" title=\"Show all publications which have a relationship to this tag\">Laplacian eigenfunctions<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=39#tppubs\" title=\"Show all publications which have a relationship to this tag\">medical imaging<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1238\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{SpatialComplexity1,<br \/>\r\ntitle = {Substrate Spatial Complexity Analysis for the Prediction of Ventricular Arrhythmias in Patients with Ischemic Cardiomyopathy},<br \/>\r\nauthor = {David Jason Miller; Jonathan Chrispin; Adityo Prakosa; Natalia Trayanova; Steven Jones; Mauro Maggioni; Katherine Wu R ; C David R. Okada},<br \/>\r\nurl = {https:\/\/www.ahajournals.org\/doi\/epub\/10.1161\/CIRCEP.119.007975},<br \/>\r\nyear  = {2020},<br \/>\r\ndate = {2020-01-01},<br \/>\r\njournal = {Circulation: Arrhythmia and Electrophysiology},<br \/>\r\nkeywords = {imaging, Laplacian eigenfunctions, medical imaging},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1238','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1238\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.ahajournals.org\/doi\/epub\/10.1161\/CIRCEP.119.007975\" title=\"https:\/\/www.ahajournals.org\/doi\/epub\/10.1161\/CIRCEP.119.007975\" target=\"_blank\">https:\/\/www.ahajournals.org\/doi\/epub\/10.1161\/CIRCEP.119.007975<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1238','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2019\">2019<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Murphy, James M;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1247','tp_links')\" style=\"cursor:pointer;\">Unsupervised Clustering and Active Learning of Hyperspectral Images With Nonlinear Diffusion<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">IEEE Transactions on Geoscience and Remote Sensing, <\/span><span class=\"tp_pub_additional_volume\">vol. 57, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 1829-1845, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>, <span class=\"tp_pub_additional_issn\">ISSN: 1558-0644<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1247\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1247','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1247\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1247','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=4#tppubs\" title=\"Show all publications which have a relationship to this tag\">Active Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=3#tppubs\" title=\"Show all publications which have a relationship to this tag\">Clustering<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20#tppubs\" title=\"Show all publications which have a relationship to this tag\">diffusion geometry<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=35#tppubs\" title=\"Show all publications which have a relationship to this tag\">hyperspectral imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34#tppubs\" title=\"Show all publications which have a relationship to this tag\">imaging<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1247\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{8481477,<br \/>\r\ntitle = {Unsupervised Clustering and Active Learning of Hyperspectral Images With Nonlinear Diffusion},<br \/>\r\nauthor = {James M Murphy and Mauro Maggioni},<br \/>\r\ndoi = {10.1109\/TGRS.2018.2869723},<br \/>\r\nissn = {1558-0644},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-03-01},<br \/>\r\nurldate = {2019-03-01},<br \/>\r\njournal = {IEEE Transactions on Geoscience and Remote Sensing},<br \/>\r\nvolume = {57},<br \/>\r\nnumber = {3},<br \/>\r\npages = {1829-1845},<br \/>\r\nkeywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1247','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1247\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1109\/TGRS.2018.2869723\" title=\"Follow DOI:10.1109\/TGRS.2018.2869723\" target=\"_blank\">doi:10.1109\/TGRS.2018.2869723<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1247','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Maggioni, Mauro;  Miller, Jason;  Zhong, Ming<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1239','tp_links')\" style=\"cursor:pointer;\">Data-driven Discovery of Emergent Behaviors in Collective Dynamics<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Physica D: Nonlinear Phenomena, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1239\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1239','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1239\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1239','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=15#tppubs\" title=\"Show all publications which have a relationship to this tag\">model reduction<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1239\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{DiscoveryEmergentBehaviors,<br \/>\r\ntitle = {Data-driven Discovery of Emergent Behaviors in Collective Dynamics},<br \/>\r\nauthor = {Mauro Maggioni and Jason Miller and Ming Zhong},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/1912.11123},<br \/>\r\ndoi = {https:\/\/doi.org\/10.1016\/j.physd.2020.132542},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\njournal = {Physica D: Nonlinear Phenomena},<br \/>\r\nkeywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1239','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1239\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/1912.11123\" title=\"https:\/\/arxiv.org\/abs\/1912.11123\" target=\"_blank\">https:\/\/arxiv.org\/abs\/1912.11123<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.1016\/j.physd.2020.132542\" title=\"Follow DOI:https:\/\/doi.org\/10.1016\/j.physd.2020.132542\" target=\"_blank\">doi:https:\/\/doi.org\/10.1016\/j.physd.2020.132542<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1239','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Little, Anna V;  Maggioni, Mauro;  Murphy, James M<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1241','tp_links')\" style=\"cursor:pointer;\">Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journ. Mach. Learn. Res., <\/span><span class=\"tp_pub_additional_volume\">vol. 21, <\/span><span class=\"tp_pub_additional_pages\">pp. 1-66, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1241\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1241','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1241\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1241','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=3#tppubs\" title=\"Show all publications which have a relationship to this tag\">Clustering<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20#tppubs\" title=\"Show all publications which have a relationship to this tag\">diffusion geometry<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=2#tppubs\" title=\"Show all publications which have a relationship to this tag\">Unsupervised Learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1241\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{PathBasedSpectralClustering,<br \/>\r\ntitle = {Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms},<br \/>\r\nauthor = {Anna V Little and Mauro Maggioni and James M Murphy},<br \/>\r\nurl = {http:\/\/jmlr.csail.mit.edu\/papers\/volume21\/18-085\/18-085.pdf},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\njournal = {Journ. Mach. Learn. Res.},<br \/>\r\nvolume = {21},<br \/>\r\npages = {1-66},<br \/>\r\nkeywords = {Clustering, diffusion geometry, Machine learning, Unsupervised Learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1241','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1241\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/jmlr.csail.mit.edu\/papers\/volume21\/18-085\/18-085.pdf\" title=\"http:\/\/jmlr.csail.mit.edu\/papers\/volume21\/18-085\/18-085.pdf\" target=\"_blank\">http:\/\/jmlr.csail.mit.edu\/papers\/volume21\/18-085\/18-085.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1241','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Browne, James Tomita Tyler M.;  Shen, Cencheng;  Chung, Jaewon;  Patsolic, Jesse L;  Falk, Benjamin;  Priebe, Carey E Yim Jason;  RandalMaggioni, Mauro Burns;  Vogelstein, Joshua T<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1242','tp_links')\" style=\"cursor:pointer;\">Sparse Projection Oblique Randomer Forests<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journ. Mach. Learn. Res., <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1242\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1242','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1242\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1242','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1242\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{SparseObliqueRandomerForests,<br \/>\r\ntitle = {Sparse Projection Oblique Randomer Forests},<br \/>\r\nauthor = {James Tomita Tyler M. Browne and Cencheng Shen and Jaewon Chung and Jesse L Patsolic and Benjamin Falk and Carey E Yim Jason Priebe and Mauro Burns RandalMaggioni and Joshua T Vogelstein},<br \/>\r\nurl = {https:\/\/arxiv.org\/pdf\/1506.03410.pdf},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\njournal = {Journ. Mach. Learn. Res.},<br \/>\r\nkeywords = {Machine learning, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1242','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1242\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/pdf\/1506.03410.pdf\" title=\"https:\/\/arxiv.org\/pdf\/1506.03410.pdf\" target=\"_blank\">https:\/\/arxiv.org\/pdf\/1506.03410.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1242','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Maggioni, Mauro;  Murphy, James M<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1243','tp_links')\" style=\"cursor:pointer;\">Learning by active nonlinear diffusion<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Foundations of Data Science, <\/span><span class=\"tp_pub_additional_volume\">vol. 1, <\/span><span class=\"tp_pub_additional_number\">no. &#8220;2639-8001-2019-3-271&#8221;, <\/span><span class=\"tp_pub_additional_pages\">pp. 271, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>, <span class=\"tp_pub_additional_issn\">ISSN: A0000-0002<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1243\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1243','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1243\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1243','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=4#tppubs\" title=\"Show all publications which have a relationship to this tag\">Active Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=3#tppubs\" title=\"Show all publications which have a relationship to this tag\">Clustering<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20#tppubs\" title=\"Show all publications which have a relationship to this tag\">diffusion geometry<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=2#tppubs\" title=\"Show all publications which have a relationship to this tag\">Unsupervised Learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1243\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{2639-8001_2019_3_271,<br \/>\r\ntitle = {Learning by active nonlinear diffusion},<br \/>\r\nauthor = {Mauro Maggioni and James M Murphy},<br \/>\r\nurl = {http:\/\/aimsciences.org\/\/article\/id\/6f8fefb2-e464-48ea-b2de-f37686725966},<br \/>\r\ndoi = {10.3934\/fods.2019012},<br \/>\r\nissn = {A0000-0002},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\njournal = {Foundations of Data Science},<br \/>\r\nvolume = {1},<br \/>\r\nnumber = {\"2639-8001-2019-3-271\"},<br \/>\r\npages = {271},<br \/>\r\nkeywords = {Active Learning, Clustering, diffusion geometry, Machine learning, Unsupervised Learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1243','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1243\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/aimsciences.org\/\/article\/id\/6f8fefb2-e464-48ea-b2de-f37686725966\" title=\"http:\/\/aimsciences.org\/\/article\/id\/6f8fefb2-e464-48ea-b2de-f37686725966\" target=\"_blank\">http:\/\/aimsciences.org\/\/article\/id\/6f8fefb2-e464-48ea-b2de-f37686725966<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.3934\/fods.2019012\" title=\"Follow DOI:10.3934\/fods.2019012\" target=\"_blank\">doi:10.3934\/fods.2019012<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1243','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Lu, Fei;  Zhong, Ming;  Tang, Sui;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1246','tp_links')\" style=\"cursor:pointer;\">Nonparametric inference of interaction laws in systems of agents from trajectory data<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Proceedings of the National Academy of Sciences, <\/span><span class=\"tp_pub_additional_volume\">vol. 116, <\/span><span class=\"tp_pub_additional_number\">no. 29, <\/span><span class=\"tp_pub_additional_pages\">pp. 14424\u201314433, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>, <span class=\"tp_pub_additional_issn\">ISSN: 0027-8424<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1246\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1246','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1246\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1246','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=16#tppubs\" title=\"Show all publications which have a relationship to this tag\">inverse problems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=15#tppubs\" title=\"Show all publications which have a relationship to this tag\">model reduction<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1246\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{LMTZ:AgentsNonParametric,<br \/>\r\ntitle = {Nonparametric inference of interaction laws in systems of agents from trajectory data},<br \/>\r\nauthor = {Fei Lu and Ming Zhong and Sui Tang and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/www.pnas.org\/content\/116\/29\/14424},<br \/>\r\ndoi = {10.1073\/pnas.1822012116},<br \/>\r\nissn = {0027-8424},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\njournal = {Proceedings of the National Academy of Sciences},<br \/>\r\nvolume = {116},<br \/>\r\nnumber = {29},<br \/>\r\npages = {14424--14433},<br \/>\r\npublisher = {National Academy of Sciences},<br \/>\r\nkeywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1246','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1246\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.pnas.org\/content\/116\/29\/14424\" title=\"https:\/\/www.pnas.org\/content\/116\/29\/14424\" target=\"_blank\">https:\/\/www.pnas.org\/content\/116\/29\/14424<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1073\/pnas.1822012116\" title=\"Follow DOI:10.1073\/pnas.1822012116\" target=\"_blank\">doi:10.1073\/pnas.1822012116<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1246','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Vogelstein, Joshua T;  Bridgeford, Eric W;  Wang, Qing;  Priebe, Carey E;  Maggioni, Mauro;  Shen, Cencheng<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1251','tp_links')\" style=\"cursor:pointer;\">Discovering and deciphering relationships across disparate data modalities<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">eLife, <\/span><span class=\"tp_pub_additional_pages\">pp. 8:e41690, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1251\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1251','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1251\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1251','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=2#tppubs\" title=\"Show all publications which have a relationship to this tag\">Unsupervised Learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1251\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{MAGC,<br \/>\r\ntitle = {Discovering and deciphering relationships across disparate data modalities},<br \/>\r\nauthor = {Joshua T Vogelstein and Eric W Bridgeford and Qing Wang and Carey E Priebe and Mauro Maggioni and Cencheng Shen},<br \/>\r\nurl = {https:\/\/elifesciences.org\/articles\/41690},<br \/>\r\ndoi = {10.7554\/eLife.41690},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\njournal = {eLife},<br \/>\r\npages = {8:e41690},<br \/>\r\nkeywords = {Machine learning, statistics, Unsupervised Learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1251','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1251\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/elifesciences.org\/articles\/41690\" title=\"https:\/\/elifesciences.org\/articles\/41690\" target=\"_blank\">https:\/\/elifesciences.org\/articles\/41690<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.7554\/eLife.41690\" title=\"Follow DOI:10.7554\/eLife.41690\" target=\"_blank\">doi:10.7554\/eLife.41690<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1251','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Liao, Wenjing;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1264','tp_links')\" style=\"cursor:pointer;\">Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of machine learning Research, <\/span><span class=\"tp_pub_additional_volume\">vol. 20, <\/span><span class=\"tp_pub_additional_number\">no. 98, <\/span><span class=\"tp_pub_additional_pages\">pp. 1-63, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1264\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1264','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1264\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1264','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=49#tppubs\" title=\"Show all publications which have a relationship to this tag\">geometric wavelets<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=27#tppubs\" title=\"Show all publications which have a relationship to this tag\">multiscale analysis<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1264\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{LiaoMaggioni:GMRA,<br \/>\r\ntitle = {Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data},<br \/>\r\nauthor = {Wenjing Liao and Mauro Maggioni},<br \/>\r\nurl = {http:\/\/jmlr.org\/papers\/v20\/17-252.html},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\njournal = {Journal of machine learning Research},<br \/>\r\nvolume = {20},<br \/>\r\nnumber = {98},<br \/>\r\npages = {1-63},<br \/>\r\nkeywords = {geometric wavelets, Machine learning, multiscale analysis, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1264','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1264\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/jmlr.org\/papers\/v20\/17-252.html\" title=\"http:\/\/jmlr.org\/papers\/v20\/17-252.html\" target=\"_blank\">http:\/\/jmlr.org\/papers\/v20\/17-252.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1264','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2018\">2018<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Escande, Paul;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\">Multiscale Approximations of Transformations <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">in preparation, <\/span><span class=\"tp_pub_additional_year\">2018<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1244\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1244','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1244\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{Escande:Muscadet,<br \/>\r\ntitle = {Multiscale Approximations of Transformations},<br \/>\r\nauthor = {Paul Escande and Mauro Maggioni},<br \/>\r\nyear  = {2018},<br \/>\r\ndate = {2018-01-01},<br \/>\r\njournal = {in preparation},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1244','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Murphy, James M;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1248','tp_links')\" style=\"cursor:pointer;\">Iterative Active Learning with Diffusion Geometry for Hyperspectral Images<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proc. of WHISPERS, <\/span><span class=\"tp_pub_additional_year\">2018<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1248\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1248','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1248\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1248','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=4#tppubs\" title=\"Show all publications which have a relationship to this tag\">Active Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=3#tppubs\" title=\"Show all publications which have a relationship to this tag\">Clustering<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20#tppubs\" title=\"Show all publications which have a relationship to this tag\">diffusion geometry<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=35#tppubs\" title=\"Show all publications which have a relationship to this tag\">hyperspectral imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34#tppubs\" title=\"Show all publications which have a relationship to this tag\">imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1248\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{whispers2018,<br \/>\r\ntitle = {Iterative Active Learning with Diffusion Geometry for Hyperspectral Images},<br \/>\r\nauthor = {James M Murphy and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/ieeexplore.ieee.org\/abstract\/document\/8747033},<br \/>\r\nyear  = {2018},<br \/>\r\ndate = {2018-01-01},<br \/>\r\nurldate = {2018-01-01},<br \/>\r\nbooktitle = {Proc. of WHISPERS},<br \/>\r\nkeywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging, Machine learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1248','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1248\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/ieeexplore.ieee.org\/abstract\/document\/8747033\" title=\"https:\/\/ieeexplore.ieee.org\/abstract\/document\/8747033\" target=\"_blank\">https:\/\/ieeexplore.ieee.org\/abstract\/document\/8747033<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1248','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Murphy, James M;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1249','tp_links')\" style=\"cursor:pointer;\">Diffusion geometric methods for fusion of remotely sensed data<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Velez-Reyes, Miguel;  Messinger, David W (Ed.): <span class=\"tp_pub_additional_booktitle\">Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIV, <\/span><span class=\"tp_pub_additional_pages\">pp. 137 \u2013 147, <\/span><span class=\"tp_pub_additional_organization\">International Society for Optics and Photonics <\/span><span class=\"tp_pub_additional_publisher\">SPIE, <\/span><span class=\"tp_pub_additional_year\">2018<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1249\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1249','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1249\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1249','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=4#tppubs\" title=\"Show all publications which have a relationship to this tag\">Active Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=3#tppubs\" title=\"Show all publications which have a relationship to this tag\">Clustering<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20#tppubs\" title=\"Show all publications which have a relationship to this tag\">diffusion geometry<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=35#tppubs\" title=\"Show all publications which have a relationship to this tag\">hyperspectral imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34#tppubs\" title=\"Show all publications which have a relationship to this tag\">imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=2#tppubs\" title=\"Show all publications which have a relationship to this tag\">Unsupervised Learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1249\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{10.1117\/12.2305274,<br \/>\r\ntitle = {Diffusion geometric methods for fusion of remotely sensed data},<br \/>\r\nauthor = {James M Murphy and Mauro Maggioni},<br \/>\r\neditor = {Miguel Velez-Reyes and David W Messinger},<br \/>\r\nurl = {https:\/\/doi.org\/10.1117\/12.2305274},<br \/>\r\ndoi = {10.1117\/12.2305274},<br \/>\r\nyear  = {2018},<br \/>\r\ndate = {2018-01-01},<br \/>\r\nurldate = {2018-01-01},<br \/>\r\nbooktitle = {Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIV},<br \/>\r\nvolume = {10644},<br \/>\r\npages = {137 -- 147},<br \/>\r\npublisher = {SPIE},<br \/>\r\norganization = {International Society for Optics and Photonics},<br \/>\r\nkeywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging, Machine learning, Unsupervised Learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1249','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1249\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/doi.org\/10.1117\/12.2305274\" title=\"https:\/\/doi.org\/10.1117\/12.2305274\" target=\"_blank\">https:\/\/doi.org\/10.1117\/12.2305274<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1117\/12.2305274\" title=\"Follow DOI:10.1117\/12.2305274\" target=\"_blank\">doi:10.1117\/12.2305274<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1249','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2017\">2017<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Maggioni, Mauro<\/p><p class=\"tp_pub_title\">Geometric Measure Estimation <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">in preparation, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1280\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1280','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=49#tppubs\" title=\"Show all publications which have a relationship to this tag\">geometric wavelets<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1280\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{CIM:geometricdensityestimation,<br \/>\r\ntitle = {Geometric Measure Estimation},<br \/>\r\nauthor = {Mauro Maggioni},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\njournal = {in preparation},<br \/>\r\nkeywords = {geometric wavelets, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1280','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Crosskey, Miles C;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1252','tp_links')\" style=\"cursor:pointer;\">ATLAS: A geometric approach to learning high-dimensional stochastic systems near manifolds<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of Multiscale Modeling and Simulation, <\/span><span class=\"tp_pub_additional_volume\">vol. 15, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 110\u2013156, <\/span><span class=\"tp_pub_additional_year\">2017<\/span><span class=\"tp_pub_additional_note\">, (arxiv: 1404.0667)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1252\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1252','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1252\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1252','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20#tppubs\" title=\"Show all publications which have a relationship to this tag\">diffusion geometry<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=7#tppubs\" title=\"Show all publications which have a relationship to this tag\">Manifold Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=23#tppubs\" title=\"Show all publications which have a relationship to this tag\">stochastic systems<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1252\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{CM:ATLAS,<br \/>\r\ntitle = {ATLAS: A geometric approach to learning high-dimensional stochastic systems near manifolds},<br \/>\r\nauthor = {Miles C Crosskey and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/1404.0667<br \/>\r\nhttps:\/\/doi.org\/10.1137\/140970951},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\njournal = {Journal of Multiscale Modeling and Simulation},<br \/>\r\nvolume = {15},<br \/>\r\nnumber = {1},<br \/>\r\npages = {110--156},<br \/>\r\nnote = {arxiv: 1404.0667},<br \/>\r\nkeywords = {diffusion geometry, Machine learning, Manifold Learning, statistics, stochastic systems},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1252','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1252\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/1404.0667\" title=\"https:\/\/arxiv.org\/abs\/1404.0667\" target=\"_blank\">https:\/\/arxiv.org\/abs\/1404.0667<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/doi.org\/10.1137\/140970951\" title=\"https:\/\/doi.org\/10.1137\/140970951\" target=\"_blank\">https:\/\/doi.org\/10.1137\/140970951<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1252','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Tomita, Tyler M;  Maggioni, Mauro;  Vogelstein, Joshua T<\/p><p class=\"tp_pub_title\">ROFLMAO: Robust Oblique Forests with Linear MAtrix Operations <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">SIAM Data Mining, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1256\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1256','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1256\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{RerF,<br \/>\r\ntitle = {ROFLMAO: Robust Oblique Forests with Linear MAtrix Operations},<br \/>\r\nauthor = {Tyler M Tomita and Mauro Maggioni and Joshua T Vogelstein},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\nbooktitle = {SIAM Data Mining},<br \/>\r\nkeywords = {Machine learning, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1256','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Tomita, Tyler;  Maggioni, Mauro;  Vogelstein, Joshua T<\/p><p class=\"tp_pub_title\">ROFLMAO: Robust Oblique Forests with Linear MAtrix Operations <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1260\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1260','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1260\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{TMJ:ROFLMAO,<br \/>\r\ntitle = {ROFLMAO: Robust Oblique Forests with Linear MAtrix Operations},<br \/>\r\nauthor = {Tyler Tomita and Mauro Maggioni and Joshua T Vogelstein},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\nkeywords = {Machine learning, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1260','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Gerber, Sam;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1265','tp_links')\" style=\"cursor:pointer;\">Multiscale Strategies for Discrete Optimal Transport<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journ. Mach. Learn. Res., <\/span><span class=\"tp_pub_additional_number\">no. 72, <\/span><span class=\"tp_pub_additional_pages\">pp. 1\u201332, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1265\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1265','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1265\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1265','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=27#tppubs\" title=\"Show all publications which have a relationship to this tag\">multiscale analysis<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=43#tppubs\" title=\"Show all publications which have a relationship to this tag\">optimal transport<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=44#tppubs\" title=\"Show all publications which have a relationship to this tag\">optimization<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1265\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{GM:mop,<br \/>\r\ntitle = {Multiscale Strategies for Discrete Optimal Transport},<br \/>\r\nauthor = {Sam Gerber and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/jmlr.csail.mit.edu\/papers\/volume18\/16-108\/16-108.pdf},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\njournal = {Journ. Mach. Learn. Res.},<br \/>\r\nnumber = {72},<br \/>\r\npages = {1--32},<br \/>\r\nkeywords = {multiscale analysis, optimal transport, optimization},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1265','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1265\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/jmlr.csail.mit.edu\/papers\/volume18\/16-108\/16-108.pdf\" title=\"https:\/\/jmlr.csail.mit.edu\/papers\/volume18\/16-108\/16-108.pdf\" target=\"_blank\">https:\/\/jmlr.csail.mit.edu\/papers\/volume18\/16-108\/16-108.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1265','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Little, Anna V;  Maggioni, Mauro;  Rosasco, Lorenzo<\/p><p class=\"tp_pub_title\">Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Applied and Computational Harmonic Analysis, <\/span><span class=\"tp_pub_additional_volume\">vol. 43, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 504 &#8211; 567, <\/span><span class=\"tp_pub_additional_year\">2017<\/span><span class=\"tp_pub_additional_note\">, (Submitted: 2012, MIT-CSAIL-TR-2012-029\/CBCL-310)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1275\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1275','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=49#tppubs\" title=\"Show all publications which have a relationship to this tag\">geometric wavelets<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=7#tppubs\" title=\"Show all publications which have a relationship to this tag\">Manifold Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=27#tppubs\" title=\"Show all publications which have a relationship to this tag\">multiscale analysis<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1275\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{LMR:MGM1,<br \/>\r\ntitle = {Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature},<br \/>\r\nauthor = {Anna V Little and Mauro Maggioni and Lorenzo Rosasco},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\njournal = {Applied and Computational Harmonic Analysis},<br \/>\r\nvolume = {43},<br \/>\r\nnumber = {3},<br \/>\r\npages = {504 - 567},<br \/>\r\nnote = {Submitted: 2012, MIT-CSAIL-TR-2012-029\/CBCL-310},<br \/>\r\nkeywords = {geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1275','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2016\">2016<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Wang, Yang;  Chen, Guangliang;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1259','tp_links')\" style=\"cursor:pointer;\">High Dimensional Data Modeling Techniques for Detection of Chemical Plumes and Anomalies in Hyperspectral Images and Movies<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">IEEE Journal of selected topics in applied Earth observations and remote sensing, <\/span><span class=\"tp_pub_additional_volume\">vol. 9, <\/span><span class=\"tp_pub_additional_number\">no. 9, <\/span><span class=\"tp_pub_additional_pages\">pp. 4316\u20134324, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1259\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1259','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1259\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1259','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=4#tppubs\" title=\"Show all publications which have a relationship to this tag\">Active Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=3#tppubs\" title=\"Show all publications which have a relationship to this tag\">Clustering<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20#tppubs\" title=\"Show all publications which have a relationship to this tag\">diffusion geometry<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=35#tppubs\" title=\"Show all publications which have a relationship to this tag\">hyperspectral imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34#tppubs\" title=\"Show all publications which have a relationship to this tag\">imaging<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1259\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{WCM:HSIandMovies,<br \/>\r\ntitle = {High Dimensional Data Modeling Techniques for Detection of Chemical Plumes and Anomalies in Hyperspectral Images and Movies},<br \/>\r\nauthor = {Yang Wang and Guangliang Chen and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/1509.07497<br \/>\r\n},<br \/>\r\ndoi = {10.1109\/JSTARS.2016.2539968},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-05-16},<br \/>\r\nurldate = {2016-05-16},<br \/>\r\njournal = {IEEE Journal of selected topics in applied Earth observations and remote sensing},<br \/>\r\nvolume = {9},<br \/>\r\nnumber = {9},<br \/>\r\npages = {4316--4324},<br \/>\r\nkeywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1259','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1259\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/1509.07497\" title=\"https:\/\/arxiv.org\/abs\/1509.07497\" target=\"_blank\">https:\/\/arxiv.org\/abs\/1509.07497<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1109\/JSTARS.2016.2539968\" title=\"Follow DOI:10.1109\/JSTARS.2016.2539968\" target=\"_blank\">doi:10.1109\/JSTARS.2016.2539968<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1259','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Shen, Cencheng;  Priebe, Carey E;  Maggioni, Mauro;  Vogelstein, Joshua T<\/p><p class=\"tp_pub_title\">Dependence Discovery from Multimodal Data via Multiscale Generalized Correlation <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Submitted, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1254\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1254','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=2#tppubs\" title=\"Show all publications which have a relationship to this tag\">Unsupervised Learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1254\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{ShenEtAl2016,<br \/>\r\ntitle = {Dependence Discovery from Multimodal Data via Multiscale Generalized Correlation},<br \/>\r\nauthor = {Cencheng Shen and Carey E Priebe and Mauro Maggioni and Joshua T Vogelstein},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {Submitted},<br \/>\r\nkeywords = {Machine learning, statistics, Unsupervised Learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1254','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Yin, Rachel;  Monson, Eric;  Honig, Elisabeth;  Daubechies, Ingrid;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\">Object recognition in art drawings: Transfer of a neural network <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proc. IEEE ICASSP, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1255\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1255','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34#tppubs\" title=\"Show all publications which have a relationship to this tag\">imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=40#tppubs\" title=\"Show all publications which have a relationship to this tag\">neural networks<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=41#tppubs\" title=\"Show all publications which have a relationship to this tag\">transfer learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1255\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{YinArtDrawings,<br \/>\r\ntitle = {Object recognition in art drawings: Transfer of a neural network},<br \/>\r\nauthor = {Rachel Yin and Eric Monson and Elisabeth Honig and Ingrid Daubechies and Mauro Maggioni},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\nbooktitle = {Proc. IEEE ICASSP},<br \/>\r\nkeywords = {imaging, Machine learning, neural networks, transfer learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1255','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_journal\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Bongini, Mattia;  Fornasier, Massimo;  Hansen, M;  Maggioni, Mauro<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1257','tp_links')\" style=\"cursor:pointer;\">Inferring Interaction Rules From Observations of Evolutive Systems I: The Variational Approach<\/a> <span class=\"tp_pub_type tp_  journal\">journal<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1257\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1257','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1257\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1257','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=14#tppubs\" title=\"Show all publications which have a relationship to this tag\">agent-based models<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=13#tppubs\" title=\"Show all publications which have a relationship to this tag\">interacting particle systems<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1257\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@journal{BFHM:LearningInteractionRulesI,<br \/>\r\ntitle = {Inferring Interaction Rules From Observations of Evolutive Systems I: The Variational Approach},<br \/>\r\nauthor = {Mattia Bongini and Massimo Fornasier and M Hansen and Mauro Maggioni},<br \/>\r\nurl = {https:\/\/arxiv.org\/pdf\/1602.00342.pdf},<br \/>\r\ndoi = {https:\/\/doi.org\/10.1142\/S0218202517500208},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {Mathematical Models and Methods in Applied Sciences},<br \/>\r\nvolume = {27},<br \/>\r\nnumber = {05},<br \/>\r\npages = {909-951},<br \/>\r\nkeywords = {agent-based models, interacting particle systems, Machine learning, statistics},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {journal}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1257','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1257\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/pdf\/1602.00342.pdf\" title=\"https:\/\/arxiv.org\/pdf\/1602.00342.pdf\" target=\"_blank\">https:\/\/arxiv.org\/pdf\/1602.00342.pdf<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.1142\/S0218202517500208\" title=\"Follow DOI:https:\/\/doi.org\/10.1142\/S0218202517500208\" target=\"_blank\">doi:https:\/\/doi.org\/10.1142\/S0218202517500208<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1257','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Liao, Wenjing;  Maggioni, Mauro;  Vigogna, S<\/p><p class=\"tp_pub_title\">Learning adaptive multiscale approximations to data and functions near low-dimensional sets <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the IEEE Information Theory Workshop, <\/span><span class=\"tp_pub_additional_year\">2016<\/span><span class=\"tp_pub_additional_note\">, (Cambridge, UK)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1263\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1263','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=7#tppubs\" title=\"Show all publications which have a relationship to this tag\">Manifold Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1263\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{LMV:IEEE2016InformationTheory,<br \/>\r\ntitle = {Learning adaptive multiscale approximations to data and functions near low-dimensional sets},<br \/>\r\nauthor = {Wenjing Liao and Mauro Maggioni and S Vigogna},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\nbooktitle = {Proceedings of the IEEE Information Theory Workshop},<br \/>\r\nnote = {Cambridge, UK},<br \/>\r\nkeywords = {Machine learning, Manifold Learning, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1263','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Maggioni, Mauro;  Minsker, Stanislav;  Strawn, Nate<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1266','tp_links')\" style=\"cursor:pointer;\">Multiscale Dictionary Learning: Non-asymptotic Bounds and Robustness<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">J. Mach. Learn. Res., <\/span><span class=\"tp_pub_additional_volume\">vol. 17, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 43\u201393, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>, <span class=\"tp_pub_additional_issn\">ISSN: 1532-4435<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1266\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1266','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1266\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1266','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=9#tppubs\" title=\"Show all publications which have a relationship to this tag\">dictionary learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=7#tppubs\" title=\"Show all publications which have a relationship to this tag\">Manifold Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=10#tppubs\" title=\"Show all publications which have a relationship to this tag\">multi-resolution analysis<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=11#tppubs\" title=\"Show all publications which have a relationship to this tag\">robustness<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=12#tppubs\" title=\"Show all publications which have a relationship to this tag\">sparsity<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1266\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{MMS:NoisyDictionaryLearning,<br \/>\r\ntitle = {Multiscale Dictionary Learning: Non-asymptotic Bounds and Robustness},<br \/>\r\nauthor = {Mauro Maggioni and Stanislav Minsker and Nate Strawn},<br \/>\r\nurl = {http:\/\/dl.acm.org\/citation.cfm?id=2946645.2946647},<br \/>\r\nissn = {1532-4435},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {J. Mach. Learn. Res.},<br \/>\r\nvolume = {17},<br \/>\r\nnumber = {1},<br \/>\r\npages = {43--93},<br \/>\r\npublisher = {JMLR.org},<br \/>\r\nkeywords = {dictionary learning, Manifold Learning, multi-resolution analysis, robustness, sparsity},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1266','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1266\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/dl.acm.org\/citation.cfm?id=2946645.2946647\" title=\"http:\/\/dl.acm.org\/citation.cfm?id=2946645.2946647\" target=\"_blank\">http:\/\/dl.acm.org\/citation.cfm?id=2946645.2946647<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1266','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><h3 class=\"tp_h3\" id=\"tp_h3_2015\">2015<\/h3><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Tomita, Tyler M;  Maggioni, Mauro;  Vogelstein, Joshua T<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1253','tp_links')\" style=\"cursor:pointer;\">Randomer Forests<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">arXiv preprint arXiv:1506.03410, <\/span><span class=\"tp_pub_additional_year\">2015<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1253\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1253','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1253\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1253','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=1#tppubs\" title=\"Show all publications which have a relationship to this tag\">Machine learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=17#tppubs\" title=\"Show all publications which have a relationship to this tag\">statistics<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=18#tppubs\" title=\"Show all publications which have a relationship to this tag\">supervised learning<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1253\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{Tomita2017b,<br \/>\r\ntitle = {Randomer Forests},<br \/>\r\nauthor = {Tyler M Tomita and Mauro Maggioni and Joshua T Vogelstein},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/1506.03410},<br \/>\r\nyear  = {2015},<br \/>\r\ndate = {2015-01-01},<br \/>\r\njournal = {arXiv preprint arXiv:1506.03410},<br \/>\r\nkeywords = {Machine learning, statistics, supervised learning},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1253','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1253\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/1506.03410\" title=\"https:\/\/arxiv.org\/abs\/1506.03410\" target=\"_blank\">https:\/\/arxiv.org\/abs\/1506.03410<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1253','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Maggioni, Mauro Y. Wang;  Chen, Guangliang<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1262','tp_links')\" style=\"cursor:pointer;\">Enhanced Detection of Chemical Plumes in Hyperspectral Images and Movies through Improved Background Modeling<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), <\/span><span class=\"tp_pub_additional_year\">2015<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1262\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1262','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_1262\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1262','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span> | <span class=\"tp_pub_tags_label\">Tags: <\/span><a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=4#tppubs\" title=\"Show all publications which have a relationship to this tag\">Active Learning<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=3#tppubs\" title=\"Show all publications which have a relationship to this tag\">Clustering<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=20#tppubs\" title=\"Show all publications which have a relationship to this tag\">diffusion geometry<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=35#tppubs\" title=\"Show all publications which have a relationship to this tag\">hyperspectral imaging<\/a>, <a rel=\"nofollow\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;tgid=34#tppubs\" title=\"Show all publications which have a relationship to this tag\">imaging<\/a><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1262\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{WangChenMaggioni:Whispers15,<br \/>\r\ntitle = {Enhanced Detection of Chemical Plumes in Hyperspectral Images and Movies through Improved Background Modeling},<br \/>\r\nauthor = {Mauro Y. Wang Maggioni and Guangliang Chen},<br \/>\r\nurl = {https:\/\/www.sjsu.edu\/faculty\/guangliang.chen\/papers\/ChenMaggioniWang_workshop.pdf},<br \/>\r\ndoi = {10.1109\/WHISPERS.2015.8075369},<br \/>\r\nyear  = {2015},<br \/>\r\ndate = {2015-01-01},<br \/>\r\nurldate = {2015-01-01},<br \/>\r\nbooktitle = {Proceedings of the 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)},<br \/>\r\nkeywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1262','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1262\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.sjsu.edu\/faculty\/guangliang.chen\/papers\/ChenMaggioniWang_workshop.pdf\" title=\"https:\/\/www.sjsu.edu\/faculty\/guangliang.chen\/papers\/ChenMaggioniWang_workshop.pd[...]\" target=\"_blank\">https:\/\/www.sjsu.edu\/faculty\/guangliang.chen\/papers\/ChenMaggioniWang_workshop.pd[&#8230;]<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1109\/WHISPERS.2015.8075369\" title=\"Follow DOI:10.1109\/WHISPERS.2015.8075369\" target=\"_blank\">doi:10.1109\/WHISPERS.2015.8075369<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1262','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><div class=\"tablenav\"><div class=\"tablenav-pages\"><span class=\"displaying-num\">115 entries<\/span> <a class=\"page-numbers button disabled\">&laquo;<\/a> <a class=\"page-numbers button disabled\">&lsaquo;<\/a> 1 of 3 <a href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;limit=2&amp;tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=&amp;tsr=#tppubs\" title=\"next page\" class=\"page-numbers button\">&rsaquo;<\/a> <a href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7&amp;limit=3&amp;tgid=&amp;yr=&amp;type=&amp;usr=&amp;auth=&amp;tsr=#tppubs\" title=\"last page\" class=\"page-numbers button\">&raquo;<\/a> <\/div><\/div><\/div>\n<div id=\"Talks\" class=\"tab\"><\/div>\n<div id=\"Tutorials\" class=\"tab\">\n<ul>\n \t<li><a href=\"Talks\/Maggioni_PKU.pdf\">Lectures at Summer School at Peking University<\/a>, July 2017.<\/li>\n \t<li>PCMI Lectures, Summer 2016: <a href=\"PCMI\/Maggioni_PCMISummerSchool_1.pdf\">Lecture 1<\/a>, <a href=\"PCMI\/Maggioni_PCMISummerSchool_2.pdf\">Lecture 2<\/a>, <a href=\"PCMI\/PCMI_Problems.pdf\">Problems\/discussion points<\/a><\/li>\n \t<li><a href=\"http:\/\/scholar.google.com\/citations?user=e6JywScAAAAJ\">Google Scholar<\/a><\/li>\n \t<li><a href=\"http:\/\/arxiv.org\/find\/all\/1\/all:+AND+mauro+maggioni\/0\/1\/0\/all\/0\/1\">Papers on the ArXiv<\/a><\/li>\n \t<li><a href=\"http:\/\/www.ams.org\/mathscinet\/search\/publications.html?pg4=AUCN&amp;s4=maggioni%2C+mauro&amp;co4=AND&amp;pg5=TI&amp;s5=&amp;co5=AND&amp;pg6=PC&amp;s6=&amp;co6=AND&amp;pg7=ALLF&amp;s7=&amp;co7=AND&amp;Submit=Search&amp;dr=all&amp;yrop=eq&amp;arg3=&amp;yearRangeFirst=&amp;yearRangeSecond=&amp;pg8=ET&amp;s8=All&amp;review_format=html\">Papers on MathsciNet<\/a><\/li>\n \t<li><a href=\"https:\/\/www.ipam.ucla.edu\/schedule.aspx?pc=mratut\">Tutorials<\/a> on diffusion geometry and multiscale analysis on graphs at the <a href=\"http:\/\/www.ipam.ucla.edu\/programs\/mra2008\/\">MRA Internet Program<\/a> at <a href=\"http:\/\/www.ipam.ucla.edu\">IPAM<\/a>: <a href=\"Talks\/MRA2008_Tutorial_I.pdf\"> Part I<\/a> and <a href=\"Talks\/MRA2008_Tutorial_II.pdf\"> Part II<\/a>.<\/li>\n \t<li><a href=\"Talks\/DiffusionWavelets_MGA_2004.pdf\">Diffusion Geometries, Diffusion Wavelets and Harmonic Analysis of large data sets<\/a>, IPAM, Multiscale Geometric Analysis Program, Fall 2004.<\/li>\n \t<li><a href=\"Talks\/DiffusionMultiscaleGeometry_IPAM.pdf\">Diffusion Geometries, global and multiscale<\/a>, IPAM, 2005.<\/li>\n<\/ul>\n<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Lectures at Summer School at Peking University, July 2017. PCMI Lectures, Summer 2016: Lecture 1, Lecture 2, Problems\/discussion points Google Scholar Papers on the ArXiv Papers on MathsciNet Tutorials on diffusion geometry and multiscale analysis on graphs at the MRA Internet Program at IPAM: Part I and Part II. Diffusion Geometries, Diffusion Wavelets and Harmonic&hellip; <a class=\"more-link\" href=\"https:\/\/mauromaggioni.duckdns.org\/?page_id=7\">Continue reading <span class=\"screen-reader-text\">Publications<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/mauromaggioni.duckdns.org\/index.php?rest_route=\/wp\/v2\/pages\/7","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mauromaggioni.duckdns.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mauromaggioni.duckdns.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mauromaggioni.duckdns.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mauromaggioni.duckdns.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7"}],"version-history":[{"count":11,"href":"https:\/\/mauromaggioni.duckdns.org\/index.php?rest_route=\/wp\/v2\/pages\/7\/revisions"}],"predecessor-version":[{"id":1186,"href":"https:\/\/mauromaggioni.duckdns.org\/index.php?rest_route=\/wp\/v2\/pages\/7\/revisions\/1186"}],"wp:attachment":[{"href":"https:\/\/mauromaggioni.duckdns.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}