2020
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Lu, Fei; Maggioni, Mauro; Tang, Sui Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories Journal Article Forthcoming arXiv, Forthcoming. Abstract | Links | BibTeX | Tags: interacting particle systems, inverse problems, Machine learning, statistics, stochastic systems @article{learningStochasticInteracting,
title = {Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories},
author = {Fei Lu and Mauro Maggioni and Sui Tang},
url = {https://arxiv.org/abs/2007.15174},
year = {2020},
date = {2020-07-31},
journal = {arXiv},
abstract = {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 gaps 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 algorithm 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.},
keywords = {interacting particle systems, inverse problems, Machine learning, statistics, stochastic systems},
pubstate = {forthcoming},
tppubtype = {article}
}
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 gaps 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 algorithm 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. |
Lanteri, Alessandro; Maggioni, Mauro; Vigogna, Stefano Conditional regression for single-index models Miscellaneous 2020. Links | BibTeX | Tags: regression, statistics @misc{aless2020conditional,
title = {Conditional regression for single-index models},
author = {Alessandro Lanteri and Mauro Maggioni and Stefano Vigogna},
url = {https://arxiv.org/abs/2002.10008},
year = {2020},
date = {2020-01-01},
keywords = {regression, statistics},
pubstate = {published},
tppubtype = {misc}
}
|
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 Sparse Projection Oblique Randomer Forests Journal Article Journal of Machine Learning Research, 21 (104), pp. 1-39, 2020. Links | BibTeX | Tags: Machine learning, statistics, supervised learning @article{SparseObliqueRandomerForestsb,
title = {Sparse Projection Oblique Randomer Forests},
author = {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},
url = {http://jmlr.org/papers/v21/18-664.html},
year = {2020},
date = {2020-01-01},
journal = {Journal of Machine Learning Research},
volume = {21},
number = {104},
pages = {1-39},
keywords = {Machine learning, statistics, supervised learning},
pubstate = {published},
tppubtype = {article}
}
|
2019
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Maggioni, Mauro; Miller, Jason; Zhong, Ming Data-driven Discovery of Emergent Behaviors in Collective Dynamics Journal Article Physica D: Nonlinear Phenomena, 2019. Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics @article{DiscoveryEmergentBehaviors,
title = {Data-driven Discovery of Emergent Behaviors in Collective Dynamics},
author = {Mauro Maggioni and Jason Miller and Ming Zhong},
url = {https://arxiv.org/abs/1912.11123},
doi = {https://doi.org/10.1016/j.physd.2020.132542},
year = {2019},
date = {2019-01-01},
journal = {Physica D: Nonlinear Phenomena},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}
|
Lu, Fei; Li, Zhongyang; Maggioni, Mauro; Tang, Sui; Zhang, Cheng On the identifiability of interaction functions in systems of interacting particles Journal Article submitted, 2019. Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics @article{IdentifiabilityInteractionFunctions,
title = {On the identifiability of interaction functions in systems of interacting particles},
author = {Fei Lu and Zhongyang Li and Mauro Maggioni and Sui Tang and Cheng Zhang},
url = {https://arxiv.org/abs/1912.11965},
year = {2019},
date = {2019-01-01},
journal = {submitted},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}
|
Browne, James Tomita Tyler M; Shen, Cencheng; Chung, Jaewon; Patsolic, Jesse L; Falk, Benjamin; Priebe, Carey Yim Jason E; RandalMaggioni, Mauro Burns; Vogelstein, Joshua T Sparse Projection Oblique Randomer Forests Journal Article Journ. Mach. Learn. Res., 2019. Links | BibTeX | Tags: Machine learning, statistics, supervised learning @article{SparseObliqueRandomerForests,
title = {Sparse Projection Oblique Randomer Forests},
author = {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},
url = {https://arxiv.org/pdf/1506.03410.pdf},
year = {2019},
date = {2019-01-01},
journal = {Journ. Mach. Learn. Res.},
keywords = {Machine learning, statistics, supervised learning},
pubstate = {published},
tppubtype = {article}
}
|
Lu, Fei; Maggioni, Mauro; Tang, Sui Learning interaction kernels in heterogeneous systems of agents from multiple trajectories Journal Article submitted, 2019. Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics @article{LMT:AgentsHeterogeneous,
title = {Learning interaction kernels in heterogeneous systems of agents from multiple trajectories},
author = {Fei Lu and Mauro Maggioni and Sui Tang},
url = {https://arxiv.org/abs/1910.04832},
year = {2019},
date = {2019-01-01},
journal = {submitted},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}
|
Lu, Fei; Zhong, Ming; Tang, Sui; Maggioni, Mauro Nonparametric inference of interaction laws in systems of agents from trajectory data Journal Article Proceedings of the National Academy of Sciences, 116 (29), pp. 14424–14433, 2019, ISSN: 0027-8424. Links | BibTeX | Tags: agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics @article{LMTZ:AgentsNonParametric,
title = {Nonparametric inference of interaction laws in systems of agents from trajectory data},
author = {Fei Lu and Ming Zhong and Sui Tang and Mauro Maggioni},
url = {https://www.pnas.org/content/116/29/14424},
doi = {10.1073/pnas.1822012116},
issn = {0027-8424},
year = {2019},
date = {2019-01-01},
journal = {Proceedings of the National Academy of Sciences},
volume = {116},
number = {29},
pages = {14424--14433},
publisher = {National Academy of Sciences},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}
|
Vogelstein, Joshua T; Bridgeford, Eric W; Wang, Qing; Priebe, Carey E; Maggioni, Mauro; Shen, Cencheng Discovering and deciphering relationships across disparate data modalities Journal Article eLife, pp. 8:e41690, 2019. Links | BibTeX | Tags: Machine learning, statistics, Unsupervised Learning @article{MAGC,
title = {Discovering and deciphering relationships across disparate data modalities},
author = {Joshua T Vogelstein and Eric W Bridgeford and Qing Wang and Carey E Priebe and Mauro Maggioni and Cencheng Shen},
url = {https://elifesciences.org/articles/41690},
doi = {10.7554/eLife.41690},
year = {2019},
date = {2019-01-01},
journal = {eLife},
pages = {8:e41690},
keywords = {Machine learning, statistics, Unsupervised Learning},
pubstate = {published},
tppubtype = {article}
}
|
Liao, Wenjing; Maggioni, Mauro; Vigogna, S Multiscale regression on intrinsically low-dimensional sets Journal Article in preparation, 2019. BibTeX | Tags: Machine learning, Manifold Learning, statistics, supervised learning @article{LiaoMaggioniVigogna:MultiscaleRegressionManifolds,
title = {Multiscale regression on intrinsically low-dimensional sets},
author = {Wenjing Liao and Mauro Maggioni and S Vigogna},
year = {2019},
date = {2019-01-01},
journal = {in preparation},
keywords = {Machine learning, Manifold Learning, statistics, supervised learning},
pubstate = {published},
tppubtype = {article}
}
|
Liao, Wenjing; Maggioni, Mauro Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data Journal Article Journal of machine learning Research, 20 (98), pp. 1-63, 2019. Links | BibTeX | Tags: geometric wavelets, Machine learning, multiscale analysis, statistics @article{LiaoMaggioni:GMRA,
title = {Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data},
author = {Wenjing Liao and Mauro Maggioni},
url = {http://jmlr.org/papers/v20/17-252.html},
year = {2019},
date = {2019-01-01},
journal = {Journal of machine learning Research},
volume = {20},
number = {98},
pages = {1-63},
keywords = {geometric wavelets, Machine learning, multiscale analysis, statistics},
pubstate = {published},
tppubtype = {article}
}
|
Lu, Fei; Maggioni, Mauro; Tang, Sui Learning interaction kernels in heterogeneous systems of agents from multiple trajectories Miscellaneous 2019. Links | BibTeX | Tags: interacting particle systems, inverse problems, Machine learning, model reduction, statistics @misc{lu2019learning,
title = {Learning interaction kernels in heterogeneous systems of agents from multiple trajectories},
author = {Fei Lu and Mauro Maggioni and Sui Tang},
url = {https://arxiv.org/abs/1910.04832},
year = {2019},
date = {2019-01-01},
keywords = {interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {misc}
}
|
2017
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Crosskey, Miles C; Maggioni, Mauro ATLAS: A geometric approach to learning high-dimensional stochastic systems near manifolds Journal Article Journal of Multiscale Modeling and Simulation, 15 (1), pp. 110–156, 2017, (arxiv: 1404.0667). BibTeX | Tags: diffusion geometry, Machine learning, Manifold Learning, statistics, stochastic systems @article{CM:ATLAS,
title = {ATLAS: A geometric approach to learning high-dimensional stochastic systems near manifolds},
author = {Miles C Crosskey and Mauro Maggioni},
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}
}
|
Tomita, Tyler M; Maggioni, Mauro; Vogelstein, Joshua T ROFLMAO: Robust Oblique Forests with Linear MAtrix Operations Inproceedings SIAM Data Mining, 2017. BibTeX | Tags: Machine learning, statistics, supervised learning @inproceedings{RerF,
title = {ROFLMAO: Robust Oblique Forests with Linear MAtrix Operations},
author = {Tyler M Tomita and Mauro Maggioni and Joshua T Vogelstein},
year = {2017},
date = {2017-01-01},
booktitle = {SIAM Data Mining},
keywords = {Machine learning, statistics, supervised learning},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Tomita, Tyler; Maggioni, Mauro; Vogelstein, Joshua T ROFLMAO: Robust Oblique Forests with Linear MAtrix Operations Inproceedings 2017. BibTeX | Tags: Machine learning, statistics, supervised learning @inproceedings{TMJ:ROFLMAO,
title = {ROFLMAO: Robust Oblique Forests with Linear MAtrix Operations},
author = {Tyler Tomita and Mauro Maggioni and Joshua T Vogelstein},
year = {2017},
date = {2017-01-01},
keywords = {Machine learning, statistics, supervised learning},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Little, Anna V; Maggioni, Mauro; Rosasco, Lorenzo Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature Journal Article Applied and Computational Harmonic Analysis, 43 (3), pp. 504 - 567, 2017, (Submitted: 2012, MIT-CSAIL-TR-2012-029/CBCL-310). BibTeX | Tags: geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, statistics @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}
}
|
Maggioni, Mauro Geometric Measure Estimation Journal Article in preparation, 2017. BibTeX | Tags: geometric wavelets, statistics @article{CIM:geometricdensityestimation,
title = {Geometric Measure Estimation},
author = {Mauro Maggioni},
year = {2017},
date = {2017-01-01},
journal = {in preparation},
keywords = {geometric wavelets, statistics},
pubstate = {published},
tppubtype = {article}
}
|
2016
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Shen, Cencheng; Priebe, Carey E; Maggioni, Mauro; Vogelstein, Joshua T Dependence Discovery from Multimodal Data via Multiscale Generalized Correlation Journal Article Submitted, 2016. BibTeX | Tags: Machine learning, statistics, Unsupervised Learning @article{ShenEtAl2016,
title = {Dependence Discovery from Multimodal Data via Multiscale Generalized Correlation},
author = {Cencheng Shen and Carey E Priebe and Mauro Maggioni and Joshua T Vogelstein},
year = {2016},
date = {2016-01-01},
journal = {Submitted},
keywords = {Machine learning, statistics, Unsupervised Learning},
pubstate = {published},
tppubtype = {article}
}
|
Bongini, Mattia; Fornasier, Massimo; Hansen, M; Maggioni, Mauro Inferring Interaction Rules From Observations of Evolutive Systems I: The Variational Approach 2016. Links | BibTeX | Tags: agent-based models, interacting particle systems, Machine learning, statistics @journal{BFHM:LearningInteractionRulesI,
title = {Inferring Interaction Rules From Observations of Evolutive Systems I: The Variational Approach},
author = {Mattia Bongini and Massimo Fornasier and M Hansen and Mauro Maggioni},
url = {https://arxiv.org/pdf/1602.00342.pdf},
doi = {https://doi.org/10.1142/S0218202517500208},
year = {2016},
date = {2016-01-01},
journal = {Mathematical Models and Methods in Applied Sciences},
volume = {27},
number = {05},
pages = {909-951},
keywords = {agent-based models, interacting particle systems, Machine learning, statistics},
pubstate = {published},
tppubtype = {journal}
}
|
Liao, Wenjing; Maggioni, Mauro; Vigogna, S Learning adaptive multiscale approximations to data and functions near low-dimensional sets Inproceedings Proceedings of the IEEE Information Theory Workshop, 2016, (Cambridge, UK). BibTeX | Tags: Machine learning, Manifold Learning, statistics, supervised learning @inproceedings{LMV:IEEE2016InformationTheory,
title = {Learning adaptive multiscale approximations to data and functions near low-dimensional sets},
author = {Wenjing Liao and Mauro Maggioni and S Vigogna},
year = {2016},
date = {2016-01-01},
booktitle = {Proceedings of the IEEE Information Theory Workshop},
note = {Cambridge, UK},
keywords = {Machine learning, Manifold Learning, statistics, supervised learning},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2015
|
Tomita, Tyler M; Maggioni, Mauro; Vogelstein, Joshua T Randomer Forests Journal Article arXiv preprint arXiv:1506.03410, 2015. Links | BibTeX | Tags: Machine learning, statistics, supervised learning @article{Tomita2017b,
title = {Randomer Forests},
author = {Tyler M Tomita and Mauro Maggioni and Joshua T Vogelstein},
url = {https://arxiv.org/abs/1506.03410},
year = {2015},
date = {2015-01-01},
journal = {arXiv preprint arXiv:1506.03410},
keywords = {Machine learning, statistics, supervised learning},
pubstate = {published},
tppubtype = {article}
}
|
2013
|
Maggioni, Mauro Geometric Estimation of Probability Measures in High Dimensions Inproceedings IEEE Asilomar Conference on Signals, Systems and Computers, 2013. BibTeX | Tags: geometric wavelets, statistics @inproceedings{MM_GeometricEstimationAsilomar,
title = {Geometric Estimation of Probability Measures in High Dimensions},
author = {Mauro Maggioni},
year = {2013},
date = {2013-01-01},
booktitle = {IEEE Asilomar Conference on Signals, Systems and Computers},
keywords = {geometric wavelets, statistics},
pubstate = {published},
tppubtype = {inproceedings}
}
|
2012
|
Allard, William K; Chen, Guangliang; Maggioni, Mauro Multi-scale geometric methods for data sets II: Geometric Multi-Resolution Analysis Journal Article Applied and Computational Harmonic Analysis, 32 (3), pp. 435–462, 2012. BibTeX | Tags: geometric wavelets, Machine learning, Manifold Learning, multiscale analysis, statistics @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}
}
|
2010
|
Chen, Guangliang; Maggioni, Mauro Multiscale Geometric Methods for Data Sets III: multiple planes Journal Article in preparation, 2010. BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis, statistics @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}
}
|
2009
|
Little, Anna V; Jung, Y -M; Maggioni, Mauro Multiscale Estimation of Intrinsic Dimensionality of Data Sets Inproceedings Proc. A.A.A.I., 2009. BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis, statistics @inproceedings{MM:MultiscaleDimensionalityEstimationAAAI,
title = {Multiscale Estimation of Intrinsic Dimensionality of Data Sets},
author = {Anna V Little and Y -M Jung and Mauro Maggioni},
year = {2009},
date = {2009-01-01},
booktitle = {Proc. A.A.A.I.},
keywords = {Machine learning, Manifold Learning, multiscale analysis, statistics},
pubstate = {published},
tppubtype = {inproceedings}
}
|
Little, Anna V; Lee, J; Jung, Y -M; Maggioni, Mauro Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale $SVD$ Inproceedings Proc. S.S.P., 2009. BibTeX | Tags: Machine learning, Manifold Learning, multiscale analysis, statistics @inproceedings{MM:MultiscaleDimensionalityEstimationSSP,
title = {Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale $SVD$},
author = {Anna V Little and J Lee and Y -M Jung and Mauro Maggioni},
year = {2009},
date = {2009-01-01},
booktitle = {Proc. S.S.P.},
keywords = {Machine learning, Manifold Learning, multiscale analysis, statistics},
pubstate = {published},
tppubtype = {inproceedings}
}
|