2021
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Felix X.-F. Ye Sichen Yang, Mauro Maggioni Nonlinear model reduction for slow-fast stochastic systems near manifolds Journal Article 2021. Abstract | Links | BibTeX | Tags: inverse problems, Machine learning, Manifold Learning, model reduction, random walks, statistics, stochastic systems @article{YYM:ATLAS2,
title = {Nonlinear model reduction for slow-fast stochastic systems near manifolds},
author = {Felix X.-F. Ye, Sichen Yang, Mauro Maggioni},
url = {https://arxiv.org/abs/2104.02120v1},
year = {2021},
date = {2021-04-05},
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}
}
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. |
Mauro Maggioni Jason Miller, Hongda Qiu Ming Zhong Learning Interaction Kernels for Agent Systems on Riemannian Manifolds Online 2021. Abstract | Links | BibTeX | Tags: agent-based models, interacting particle systems, Machine learning, model reduction, statistics @online{AgentSystemsManifolds,
title = { Learning Interaction Kernels for Agent Systems on Riemannian Manifolds},
author = {Mauro Maggioni, Jason Miller, Hongda Qiu, Ming Zhong},
url = {https://arxiv.org/abs/2102.00327},
year = {2021},
date = {2021-01-30},
abstract = {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 Poincaré disk model of hyperbolic space.},
keywords = {agent-based models, interacting particle systems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {online}
}
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 Poincaré disk model of hyperbolic space. |
2020
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Lu, Fei; Li, Zhongyang; Maggioni, Mauro; Tang, Sui; Zhang, Cheng On the identifiability of interaction functions in systems of interacting particles Journal Article Forthcoming to appear in Stochastic Processes and their Applications, Forthcoming. 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 = {2020},
date = {2020-10-09},
journal = {to appear in Stochastic Processes and their Applications},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {forthcoming},
tppubtype = {article}
}
|
Fei Lu Mauro Maggioni, Sui Tang Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories Journal Article Forthcoming Foundation of Computational Mathematics, Forthcoming. Abstract | Links | BibTeX | Tags: agent-based models, interacting particle systems, Machine learning, statistics, stochastic systems @article{learningStochasticInteracting,
title = {Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories},
author = {Fei Lu, Mauro Maggioni, Sui Tang},
url = {https://arxiv.org/abs/2007.15174},
year = {2020},
date = {2020-07-15},
journal = {Foundation of Computational Mathematics},
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 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.},
keywords = {agent-based models, interacting particle systems, 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 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. |
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}
}
|
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; 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}
}
|
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). Links | 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},
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}
}
|
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}
}
|
0000
|
Lu, Fei; Maggioni, Mauro; Tang, Sui Learning interaction kernels in heterogeneous systems of agents from multiple trajectories Journal Article Journ. Mach. Learn. Res., 22 (32), pp. 1–67, 0000. 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://jmlr.csail.mit.edu/papers/volume22/19-861/19-861.pdf},
journal = {Journ. Mach. Learn. Res.},
volume = {22},
number = {32},
pages = {1–67},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}
|