Publications

@article{LearningTransitionOperators_1,

title = {Learning Transition Operators From Sparse Space-Time Samples},

author = {Christian Kuemmerle and Mauro Maggioni and Sui Tang},

url = {https://arxiv.org/abs/2212.00746

https://ieeexplore.ieee.org/document/10558780},

doi = {10.1109/TIT.2024.3413534},

year  = {2024},

date = {2024-06-14},

urldate = {2024-06-14},

journal = {IEEE Transactions on Information Theory},

abstract = {We consider the nonlinear inverse problem of learning a transition operator A from partial observations at different times, in particular from sparse observations of entries of its powers A,A2,⋯,AT. This Spatio-Temporal Transition Operator Recovery problem is motivated by the recent interest in learning time-varying graph signals that are driven by graph operators depending on the underlying graph topology. We address the nonlinearity of the problem by embedding it into a higher-dimensional space of suitable block-Hankel matrices, where it becomes a low-rank matrix completion problem, even if A is of full rank. For both a uniform and an adaptive random space-time sampling model, we quantify the recoverability of the transition operator via suitable measures of incoherence of these block-Hankel embedding matrices. For graph transition operators these measures of incoherence depend on the interplay between the dynamics and the graph topology. We develop a suitable non-convex iterative reweighted least squares (IRLS) algorithm, establish its quadratic local convergence, and show that, in optimal scenarios, no more than (rnlog(nT)) space-time samples are sufficient to ensure accurate recovery of a rank-r operator A of size n×n. This establishes that spatial samples can be substituted by a comparable number of space-time samples. We provide an efficient implementation of the proposed IRLS algorithm with space complexity of order O(rnT) and per-iteration time complexity linear in n. Numerical experiments for transition operators based on several graph models confirm that the theoretical findings accurately track empirical phase transitions, and illustrate the applicability and scalability of the proposed algorithm.},

keywords = {dynamical systems, Machine learning, optimization, sparsity, statistics},

pubstate = {published},

tppubtype = {article}

}

@article{PCAlocaltransitionmatrices,

title = {Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference},

author = {E Bayrakta and F Lu and M Maggioni and R Wu and S Yang

},

url = {https://arxiv.org/html/2405.02928v2},

year  = {2024},

date = {2024-05-03},

urldate = {2024-05-03},

journal = {arXiv preprint arXiv:2405.02928},

keywords = {inverse problems, Machine learning, statistics},

pubstate = {published},

tppubtype = {article}

}

@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 = {2023-06-13},

urldate = {2023-11-04},

journal = {J Nonlinear Sci},

volume = {34},

number = {22},

issue = {1},

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, random walks, statistics, Unsupervised Learning},

pubstate = {published},

tppubtype = {article}

}

@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{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},

doi = {10.3150/22-BEJ1482},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Bernoulli},

keywords = {regression, statistics},

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{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{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}

}

@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}

}

@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}

}

@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}

}

@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}

}

@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}

}

@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}

}

@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{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}

}

@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}

}

@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}

}

@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{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{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}

}