Publications

@article{nokey,

title = {Unsupervised learning of observation functions in state-space models by nonparametric moment methods},

author = {Qingci An and Yannis Kevrekidis and Fei Lu and Mauro Maggioni},

url = {https://arxiv.org/abs/2207.05242

https://doi.org/10.3934/fods.2023002},

doi = {10.3934/fods.2023002},

year  = {2023},

date = {2023-02-01},

urldate = {2023-02-01},

journal = {Foundations of Data Science},

keywords = {computational mathematics, hidden Markov models, inverse problems, Machine learning, optimal transport, regression, statistics, stochastic systems, Unsupervised Learning},

pubstate = {published},

tppubtype = {article}

}

@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

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 = {2021-04-01},

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}

}

@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{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{CKLMN:DiffusionMapsReductionCoordinates,

title = {Diffusion Maps, reduction coordinates and low dimensional representation of stochastic systems},

author = {Ronald R Coifman and Ioannis G Kevrekidis and Stephane Lafon and Mauro Maggioni and Boaz Nadler},

year  = {2008},

date = {2008-01-01},

journal = {SIAM J.M.M.S.},

volume = {7},

number = {2},

pages = {842--864},

keywords = {diffusion geometry, dynamical systems, Laplacian eigenfunctions, Machine learning, model reduction, stochastic systems},

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{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}

}