Publications

@article{DIMON2024,

title = {DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains},

author = {Minglang Yin and Nicolas Charon and Ryan Brody and Lu Lu and Natalia Trayanova and Mauro Maggioni},

url = {https://arxiv.org/pdf/2402.07250.pdf},

year  = {2024},

date = {2024-02-13},

urldate = {2024-02-13},

journal = {arXiv},

keywords = {Machine learning, neural networks, PDEs, precision medicine},

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 = {2023-11-04},

urldate = {2023-11-04},

journal = {J Nonlinear Sci},

volume = {34},

issue = {22},

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}

}

@article{LearningInteractionkernels2ndorder,

title = {Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems},

author = {Jason Miller and Sui Tang and Ming Zhong and Mauro Maggioni},

url = {https://arxiv.org/abs/2010.03729},

doi = {https://doi.org/10.1007/s43670-023-00055-9},

year  = {2023},

date = {2023-04-12},

urldate = {2023-04-12},

journal = { Sampling Theory, Signal Processing, and Data Analysis },

volume = {21},

keywords = {agent-based models, interacting particle systems, inverse problems, Machine 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{nokey,

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},

year  = {2022},

date = {2022-12-01},

urldate = {2022-12-01},

journal = {submitted},

keywords = {},

pubstate = {forthcoming},

tppubtype = {article}

}

@article{SCDsurvival1,

title = {Arrhythmic sudden death survival prediction using deep learning analysis of scarring in the heart},

author = {Dan M. Popescu and Julie K. Shade and Changxin Lai and Konstantinos N. Aronis and David Ouyang, and M. Vinayaga Moorthy and Nancy R. Cook and Daniel C. Lee and Alan Kadish and Christine M. Albert and Katherine C. Wu and Mauro Maggioni and Natalia A. Trayanova

},

url = {https://rdcu.be/cKSAl},

doi = {10.1038/s44161-022-00041-9},

year  = {2022},

date = {2022-03-07},

urldate = {2022-03-07},

journal = {Nature Cardiovascular Research},

keywords = {Machine learning, medical imaging, neural networks, precision medicine},

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{AnatLGECMRInn,

title = {Anatomically-Informed Deep Learning on Contrast-Enhanced Cardiac MRI for Scar Segmentation and Clinical Feature Extraction},

author = {Haley G. Abramson and Dan M. Popescu and Rebecca Yu and Changxin Lai and Julie K. Shade and Katherine C. Wu and Mauro Maggioni and Natalia A. Trayanova},

url = {https://arxiv.org/abs/2010.11081

https://www.cvdigitalhealthjournal.com/article/S2666-6936(21)00131-6/pdf

https://www.ahajournals.org/doi/abs/10.1161/circ.142.suppl_3.16017

http://jhu.technologypublisher.com/technology/43121},

doi = {https://doi.org/10.1016/j.cvdhj.2021.11.007},

year  = {2021},

date = {2021-11-25},

urldate = {2021-11-25},

journal = {Cardiovascular Digital Health Journal},

keywords = {imaging, Machine learning, medical imaging},

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{LuMMTang21,

title = {Learning interaction kernels in heterogeneous systems of agents from multiple trajectories},

author = {Fei Lu, Mauro Maggioni, Sui Tang},

url = {https://jmlr.csail.mit.edu/papers/v22/19-861.html},

year  = {2021},

date = {2021-01-01},

journal = {Journ. Mach. Learn. res.},

volume = {2},

number = {32},

pages = {1--67},

abstract = {Systems of interacting particles, or agents, have wide applications in many disciplines, including Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from observation data is a fundamental task that can provide meaningful insights and accurate predictions of the behaviour of the agents. In this paper, we consider the inverse problem of learning interaction laws given data from multiple trajectories, in a nonparametric fashion, when the interaction kernels depend on pairwise distances. We establish a condition for learnability of interaction kernels, and construct an estimator based on the minimization of a suitably regularized least squares functional, that is guaranteed to converge, in a suitable L^2 space, at the optimal min-max rate for 1-dimensional nonparametric regression. We propose an efficient learning algorithm to construct such estimator, which can be implemented in parallel for multiple trajectories and is therefore well-suited for the high dimensional, big data regime. Numerical simulations on a variety examples, including opinion dynamics, predator-prey and swarm dynamics and heterogeneous particle dynamics, suggest that the learnability condition is satisfied in models used in practice, and the rate of convergence of our estimator is consistent with the theory. These simulations also suggest that our estimators are robust to noise in the observations, and can produce accurate predictions of trajectories in large time intervals, even when they are learned from observations in short time intervals.},

keywords = {Active Learning, interacting particle systems, inverse problems, Machine learning},

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{SpatialComplexity1,

title = {Substrate Spatial Complexity Analysis for the Prediction of Ventricular Arrhythmias in Patients with Ischemic Cardiomyopathy},

author = {David Jason Miller; Jonathan Chrispin; Adityo Prakosa; Natalia Trayanova; Steven Jones; Mauro Maggioni; Katherine Wu R ; C David R. Okada},

url = {https://www.ahajournals.org/doi/epub/10.1161/CIRCEP.119.007975},

year  = {2020},

date = {2020-01-01},

journal = {Circulation: Arrhythmia and Electrophysiology},

keywords = {imaging, Laplacian eigenfunctions, medical imaging},

pubstate = {published},

tppubtype = {article}

}

@article{8481477,

title = {Unsupervised Clustering and Active Learning of Hyperspectral Images With Nonlinear Diffusion},

author = {James M Murphy and Mauro Maggioni},

doi = {10.1109/TGRS.2018.2869723},

issn = {1558-0644},

year  = {2019},

date = {2019-03-01},

urldate = {2019-03-01},

journal = {IEEE Transactions on Geoscience and Remote Sensing},

volume = {57},

number = {3},

pages = {1829-1845},

keywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging},

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{PathBasedSpectralClustering,

title = {Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms},

author = {Anna V Little and Mauro Maggioni and James M Murphy},

url = {http://jmlr.csail.mit.edu/papers/volume21/18-085/18-085.pdf},

year  = {2019},

date = {2019-01-01},

journal = {Journ. Mach. Learn. Res.},

volume = {21},

pages = {1-66},

keywords = {Clustering, diffusion geometry, Machine learning, Unsupervised Learning},

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{2639-8001_2019_3_271,

title = {Learning by active nonlinear diffusion},

author = {Mauro Maggioni and James M Murphy},

url = {http://aimsciences.org//article/id/6f8fefb2-e464-48ea-b2de-f37686725966},

doi = {10.3934/fods.2019012},

issn = {A0000-0002},

year  = {2019},

date = {2019-01-01},

journal = {Foundations of Data Science},

volume = {1},

number = {"2639-8001-2019-3-271"},

pages = {271},

keywords = {Active Learning, Clustering, diffusion geometry, Machine learning, Unsupervised 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{Escande:Muscadet,

title = {Multiscale Approximations of Transformations},

author = {Paul Escande and Mauro Maggioni},

year  = {2018},

date = {2018-01-01},

journal = {in preparation},

keywords = {},

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{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{GM:mop,

title = {Multiscale Strategies for Discrete Optimal Transport},

author = {Sam Gerber and Mauro Maggioni},

url = {https://jmlr.csail.mit.edu/papers/volume18/16-108/16-108.pdf},

year  = {2017},

date = {2017-01-01},

journal = {Journ. Mach. Learn. Res.},

number = {72},

pages = {1--32},

keywords = {multiscale analysis, optimal transport, optimization},

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{WCM:HSIandMovies,

title = {High Dimensional Data Modeling Techniques for Detection of Chemical Plumes and Anomalies in Hyperspectral Images and Movies},

author = {Yang Wang and Guangliang Chen and Mauro Maggioni},

url = {https://arxiv.org/abs/1509.07497

},

doi = {10.1109/JSTARS.2016.2539968},

year  = {2016},

date = {2016-05-16},

urldate = {2016-05-16},

journal = {IEEE Journal of selected topics in applied Earth observations and remote sensing},

volume = {9},

number = {9},

pages = {4316--4324},

keywords = {Active Learning, Clustering, diffusion geometry, hyperspectral imaging, imaging},

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{MMS:NoisyDictionaryLearning,

title = {Multiscale Dictionary Learning: Non-asymptotic Bounds and Robustness},

author = {Mauro Maggioni and Stanislav Minsker and Nate Strawn},

url = {http://dl.acm.org/citation.cfm?id=2946645.2946647},

issn = {1532-4435},

year  = {2016},

date = {2016-01-01},

journal = {J. Mach. Learn. Res.},

volume = {17},

number = {1},

pages = {43--93},

publisher = {JMLR.org},

keywords = {dictionary learning, Manifold Learning, multi-resolution analysis, robustness, sparsity},

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{10.1371/journal.pcbi.1003628,

title = {Genomic Characterization of Large Heterochromatic Gaps in the Human Genome Assembly},

author = {Nicolas Altemose and Karen H Miga and Mauro Maggioni and Huntington F Willard},

url = {http://dx.doi.org/10.1371%2Fjournal.pcbi.1003628},

doi = {10.1371/journal.pcbi.1003628},

year  = {2014},

date = {2014-01-01},

journal = {PLoS Comput Biol},

volume = {10},

number = {5},

pages = {e1003628},

publisher = {Public Library of Science},

keywords = {spectral clustering},

pubstate = {published},

tppubtype = {article}

}

@article{IM:GMRA_CS,

title = {Approximation of points on low-dimensional manifolds via random linear projections},

author = {Mark A Iwen and Mauro Maggioni},

year  = {2013},

date = {2013-01-01},

journal = {Inference and Information},

volume = {2},

number = {1},

pages = {1--31},

note = {arXiv:1204.3337v1, 2012},

keywords = {Machine learning, Manifold Learning, multiscale analysis},

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}

}