Publications

@article{YYM:ATLAS2,

title = {Nonlinear model reduction for slow-fast stochastic systems near manifolds},

author = {Felix X.-F. Ye and Sichen Yang and Mauro Maggioni},

url = {https://arxiv.org/abs/2104.02120v1},

doi = {https://doi.org/10.1007/s43670-023-00055-9},

year  = {2023},

date = {2023-11-04},

urldate = {2023-11-04},

journal = {J Nonlinear Sci},

volume = {34},

issue = {22},

abstract = {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.},

keywords = {inverse problems, Machine learning, Manifold Learning, model reduction, random walks, statistics, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{LiaoMaggioniVigogna:MultiscaleRegressionManifolds,

title = {Multiscale regression on intrinsically low-dimensional sets},

author = {Wenjing Liao and Mauro Maggioni and Stefano Vigogna},

url = {https://arxiv.org/abs/2101.05119v1

http://www.aimspress.com/aimspress-data/mine/2022/4/PDF/mine-04-04-028.pdf},

doi = {DOI:10.3934/mine.2022028},

year  = {2021},

date = {2021-08-24},

urldate = {2021-08-24},

journal = {Mathematics in Engineering},

volume = {4},

number = {4},

keywords = {Machine learning, Manifold Learning, statistics, supervised learning},

pubstate = {published},

tppubtype = {article}

}

@article{CM:ATLAS,

title = {ATLAS: A geometric approach to learning high-dimensional stochastic systems near manifolds},

author = {Miles C Crosskey and Mauro Maggioni},

url = {https://arxiv.org/abs/1404.0667

https://doi.org/10.1137/140970951},

year  = {2017},

date = {2017-01-01},

journal = {Journal of Multiscale Modeling and Simulation},

volume = {15},

number = {1},

pages = {110--156},

note = {arxiv: 1404.0667},

keywords = {diffusion geometry, Machine learning, Manifold Learning, statistics, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{LMR:MGM1,

title = {Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature},

author = {Anna V Little and Mauro Maggioni and Lorenzo Rosasco},

year  = {2017},

date = {2017-01-01},

journal = {Applied and Computational Harmonic Analysis},

volume = {43},

number = {3},

pages = {504 - 567},

note = {Submitted: 2012, MIT-CSAIL-TR-2012-029/CBCL-310},

keywords = {geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, statistics},

pubstate = {published},

tppubtype = {article}

}

@article{MMS:NoisyDictionaryLearning,

title = {Multiscale Dictionary Learning: Non-asymptotic Bounds and Robustness},

author = {Mauro Maggioni and Stanislav Minsker and Nate Strawn},

url = {http://dl.acm.org/citation.cfm?id=2946645.2946647},

issn = {1532-4435},

year  = {2016},

date = {2016-01-01},

journal = {J. Mach. Learn. Res.},

volume = {17},

number = {1},

pages = {43--93},

publisher = {JMLR.org},

keywords = {dictionary learning, Manifold Learning, multi-resolution analysis, robustness, sparsity},

pubstate = {published},

tppubtype = {article}

}

@article{IM:GMRA_CS,

title = {Approximation of points on low-dimensional manifolds via random linear projections},

author = {Mark A Iwen and Mauro Maggioni},

year  = {2013},

date = {2013-01-01},

journal = {Inference and Information},

volume = {2},

number = {1},

pages = {1--31},

note = {arXiv:1204.3337v1, 2012},

keywords = {Machine learning, Manifold Learning, multiscale analysis},

pubstate = {published},

tppubtype = {article}

}

@article{CM:MGM2,

title = {Multi-scale geometric methods for data sets II: Geometric Multi-Resolution Analysis},

author = {William K Allard and Guangliang Chen and Mauro Maggioni},

year  = {2012},

date = {2012-01-01},

journal = {Applied and Computational Harmonic Analysis},

volume = {32},

number = {3},

pages = {435--462},

keywords = {geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, statistics},

pubstate = {published},

tppubtype = {article}

}

@article{FFT2011,

title = {Multi-Resolution Geometric Analysis for data in high dimensions},

author = {Guangliang Chen and Anna V Little and Mauro Maggioni},

year  = {2011},

date = {2011-08-01},

journal = {Proc. FFT 2011},

keywords = {geometric wavelets, Machine learning, Manifold Learning, multiscale analysis},

pubstate = {published},

tppubtype = {article}

}

@article{MM:Spars11talk,

title = {Multiscale Geometric Dictionaries for Point-Cloud Data, Presented at SPARS 11, http://www.math.duke.edu/~mauro/research.html#Talks},

author = {Mauro Maggioni},

url = {http://www.math.duke.edu/~mauro/research.html#Talks},

year  = {2011},

date = {2011-06-01},

note = {Presented at SPARS 11},

keywords = {dictionary learning, geometric wavelets, Machine learning, Manifold Learning, multiscale analysis},

pubstate = {published},

tppubtype = {article}

}

@article{ZRMC:PolymerReversal,

title = {Polymer reversal rate calculated via locally scaled diffusion map},

author = {W Zheng and M A Rohrdanz and Mauro Maggioni and Cecilia Clementi},

year  = {2011},

date = {2011-01-01},

journal = {J. Chem. Phys.},

number = {134},

pages = {144108},

keywords = {diffusion geometry, Machine learning, Manifold Learning, molecular dynamics, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{RZMC:ReactionCoordinatesLocalScaling,

title = {Determination of reaction coordinates via locally scaled diffusion map},

author = {M A Rohrdanz and W Zheng and Mauro Maggioni and Cecilia Clementi},

year  = {2011},

date = {2011-01-01},

journal = {J. Chem. Phys.},

number = {134},

pages = {124116},

keywords = {diffusion geometry, Machine learning, Manifold Learning, molecular dynamics, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{jms:UniformizationEigenfunctions2,

title = {Universal local manifold parametrizations via heat kernels and eigenfunctions of the Laplacian},

author = {Peter W Jones and Mauro Maggioni and Raanan Schul},

year  = {2010},

date = {2010-01-01},

journal = {Ann. Acad. Scient. Fen.},

volume = {35},

pages = {1--44},

note = {http://arxiv.org/abs/0709.1975},

keywords = {diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{CM:MGM3,

title = {Multiscale Geometric Methods for Data Sets III: multiple planes},

author = {Guangliang Chen and Mauro Maggioni},

year  = {2010},

date = {2010-01-01},

journal = {in preparation},

keywords = {Machine learning, Manifold Learning, multiscale analysis, statistics},

pubstate = {published},

tppubtype = {article}

}

@article{CM:geometricwaveletsciss,

title = {Multiscale Geometric Wavelets for the Analysis of Point Clouds},

author = {Guangliang Chen and Mauro Maggioni},

year  = {2010},

date = {2010-01-01},

journal = {Proc. CISS 2010},

keywords = {geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{SMC:GeneralFrameworkAdaptiveRegularization,

title = {Regularization on Graphs with Function-adapted Diffusion Processes},

author = {Arthur D Szlam and Mauro Maggioni and Ronald R Coifman},

url = {https://jmlr.csail.mit.edu/papers/volume9/szlam08a/szlam08a.pdf},

year  = {2008},

date = {2008-08-01},

urldate = {2008-08-01},

journal = {Jour. Mach. Learn. Res.},

number = {9},

pages = {1711--1739},

note = {(YALE/DCS/TR1365, Yale Univ, July 2006)},

keywords = {diffusion geometry, Machine learning, Manifold Learning, random walks, semisupervised learning, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{jms:UniformizationEigenfunctions,

title = {Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels},

author = {Peter W Jones and Mauro Maggioni and Raanan Schul},

year  = {2008},

date = {2008-02-01},

journal = {Proc. Nat. Acad. Sci.},

volume = {105},

number = {6},

pages = {1803--1808},

keywords = {diffusion geometry, heat kernels, Laplacian eigenfunctions, Manifold Learning, multiscale analysis, random walks, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{CM:MsDataDiffWavelets,

title = {Multiscale Data Analysis with Diffusion Wavelets},

author = {Ronald R Coifman and Mauro Maggioni},

year  = {2007},

date = {2007-04-01},

journal = {Proc. SIAM Bioinf. Workshop, Minneapolis},

keywords = {diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{smmm:jmrl1,

title = {Proto-value Functions: A Spectral Framework for Solving Markov Decision Processes},

author = {Sridhar Mahadevan and Mauro Maggioni},

year  = {2007},

date = {2007-01-01},

journal = {JMLR},

volume = {8},

pages = {2169--2231},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, reinforcement learning, representation learning, spectral graph theory},

pubstate = {published},

tppubtype = {article}

}

@article{CMDiffusionWavelets,

title = {Diffusion Wavelets},

author = {Ronald R Coifman and Mauro Maggioni},

year  = {2006},

date = {2006-07-01},

journal = {Appl. Comp. Harm. Anal.},

volume = {21},

number = {1},

pages = {53--94},

note = {(Tech. Rep. YALE/DCS/TR-1303, Yale Univ., Sep. 2004)},

keywords = {diffusion geometry, diffusion wavelets, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{DiffusionWaveletPackets,

title = {Diffusion Wavelet Packets},

author = {James Jr. C Bremer and Ronald R Coifman and Mauro Maggioni and Arthur D Szlam},

year  = {2006},

date = {2006-07-01},

journal = {Appl. Comp. Harm. Anal.},

volume = {21},

number = {1},

pages = {95--112},

note = {(Tech. Rep. YALE/DCS/TR-1304, 2004)},

keywords = {diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{CMZK:CONB,

title = {Geometric diffusions for the analysis of data from sensor networks},

author = {Ronald R Coifman and Mauro Maggioni and Steven W Zucker and Ioannis G Kevrekidis},

year  = {2005},

date = {2005-10-01},

journal = {Curr Opin Neurobiol},

volume = {15},

number = {5},

pages = {576--84},

keywords = {diffusion geometry, Laplacian eigenfunctions, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{DiffusionPNAS,

title = {Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps},

author = {Ronald R Coifman and Stephane Lafon and Ann B Lee and Mauro Maggioni and B Nadler and Frederick Warner and Steven W Zucker},

year  = {2005},

date = {2005-01-01},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

volume = {102},

number = {21},

pages = {7426-7431},

keywords = {diffusion geometry, Machine learning, Manifold Learning, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}

@article{DiffusionPNAS2,

title = {Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods},

author = {Ronald R Coifman and S Lafon and A B Lee and Mauro Maggioni and B Nadler and Frederick Warner and Steven W Zucker},

year  = {2005},

date = {2005-01-01},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

volume = {102},

number = {21},

pages = {7432--7438},

keywords = {diffusion geometry, Machine learning, Manifold Learning, multiscale analysis, random walks, spectral graph theory, stochastic systems},

pubstate = {published},

tppubtype = {article}

}