2022
Feng, Jinchao; Maggioni, Mauro; Martin, Patrick; Zhong, Ming
Learning Interaction Variables and Kernels from Observations of Agent-Based Systems Proceeding Forthcoming
Forthcoming.
Abstract | Links | BibTeX | Tags: agent-based models, inverse problems, Machine learning, statistics
@proceedings{nokey,
title = {Learning Interaction Variables and Kernels from Observations of Agent-Based Systems},
author = {Jinchao Feng and Mauro Maggioni and Patrick Martin and Ming Zhong},
url = {https://arxiv.org/abs/2208.02758},
year = {2022},
date = {2022-08-04},
urldate = {2022-08-04},
journal = {arXiV preprint},
abstract = {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.},
keywords = {agent-based models, inverse problems, Machine learning, statistics},
pubstate = {forthcoming},
tppubtype = {proceedings}
}
Lanteri, Alessandro; Maggioni, Mauro; Vigogna, Stefano
Conditional regression for single-index models Journal Article Forthcoming
In: Bernoulli, Forthcoming.
Links | BibTeX | Tags: regression, statistics
@article{aless2020conditional,
title = {Conditional regression for single-index models},
author = {Alessandro Lanteri and Mauro Maggioni and Stefano Vigogna},
url = {https://www.e-publications.org/ims/submission/BEJ/user/submissionFile/49273?confirm=22a655d7
https://arxiv.org/abs/2002.10008},
year = {2022},
date = {2022-01-01},
urldate = {2020-01-01},
journal = {Bernoulli},
keywords = {regression, statistics},
pubstate = {forthcoming},
tppubtype = {article}
}
2021
Liao, Wenjing; Maggioni, Mauro; Vigogna, Stefano
Multiscale regression on intrinsically low-dimensional sets Journal Article
In: Mathematics in Engineering, vol. 4, no. 4, 2021.
Links | 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 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}
}
Sichen Yang Felix X.-F. Ye, Mauro Maggioni
Nonlinear model reduction for slow-fast stochastic systems near manifolds Journal Article
In: 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}
}
Mauro Maggioni Fei Lu, Sui Tang
Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories Journal Article
In: Foundation of Computational Mathematics, 2021.
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
https://link.springer.com/content/pdf/10.1007/s10208-021-09521-z.pdf},
doi = {doi.org/10.1007/s10208-021-09521-z},
year = {2021},
date = {2021-04-01},
urldate = {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 = {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
In: Stochastic Processes and their Applications, vol. 132, 2021.
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},
doi = {https://doi.org/10.1016/j.spa.2020.10.005},
year = {2021},
date = {2021-02-01},
journal = {Stochastic Processes and their Applications},
volume = {132},
keywords = {agent-based models, interacting particle systems, inverse problems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {article}
}
Jason Miller Mauro Maggioni, Hongda Qiu
Learning Interaction Kernels for Agent Systems on Riemannian Manifolds Proceeding
ICML, 2021.
Abstract | Links | BibTeX | Tags: agent-based models, interacting particle systems, Machine learning, model reduction, statistics
@proceedings{AgentSystemsManifolds,
title = { Learning Interaction Kernels for Agent Systems on Riemannian Manifolds},
author = {Mauro Maggioni, Jason Miller, Hongda Qiu, Ming Zhong},
url = {http://proceedings.mlr.press/v139/maggioni21a.html
https://arxiv.org/abs/2102.00327},
year = {2021},
date = {2021-01-30},
urldate = {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.},
howpublished = {ICML},
keywords = {agent-based models, interacting particle systems, Machine learning, model reduction, statistics},
pubstate = {published},
tppubtype = {proceedings}
}
2020
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
In: Journal of Machine Learning Research, vol. 21, no. 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
Maggioni, Mauro; Miller, Jason; Zhong, Ming
Data-driven Discovery of Emergent Behaviors in Collective Dynamics Journal Article
In: 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 E Yim Jason; RandalMaggioni, Mauro Burns; Vogelstein, Joshua T
Sparse Projection Oblique Randomer Forests Journal Article
In: 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
In: Proceedings of the National Academy of Sciences, vol. 116, no. 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
In: 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
Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data Journal Article
In: Journal of machine learning Research, vol. 20, no. 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
Crosskey, Miles C; Maggioni, Mauro
ATLAS: A geometric approach to learning high-dimensional stochastic systems near manifolds Journal Article
In: Journal of Multiscale Modeling and Simulation, vol. 15, no. 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
In: 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
In: 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
In: Applied and Computational Harmonic Analysis, vol. 43, no. 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: 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
Shen, Cencheng; Priebe, Carey E; Maggioni, Mauro; Vogelstein, Joshua T
Dependence Discovery from Multimodal Data via Multiscale Generalized Correlation Journal Article
In: 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 journal
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
In: 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
In: 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
In: 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
In: Applied and Computational Harmonic Analysis, vol. 32, no. 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: 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
In: 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
In: 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
In: Journ. Mach. Learn. Res., vol. 22, no. 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}
}
- 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 Analysis of large data sets, IPAM, Multiscale Geometric Analysis Program, Fall 2004.
- Diffusion Geometries, global and multiscale, IPAM, 2005.