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{DIMON2024,

title = {A scalable framework for learning the geometry-dependent solution operators of partial differential equations},

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

https://www.nature.com/articles/s43588-024-00732-2

https://rdcu.be/d2UPp

https://github.com/MinglangYin/DIMON},

doi = {10.1038/s43588-024-00732-2},

year  = {2024},

date = {2024-02-13},

urldate = {2024-02-13},

journal = {Nature Computational Science},

abstract = {The solution of a PDE over varying initial/boundary conditions on multiple domains is needed in a wide variety of applications, but it is computationally expensive if the solution is computed de novo whenever the initial/boundary conditions of the domain change. We introduce a general operator learning framework, called DIffeomorphic Mapping Operator learNing (DIMON) to learn approximate PDE solutions over a family of domains ${Omega_{theta}}_theta$, that learns the map from initial/boundary conditions and domain $Omega_theta$ to the solution of the PDE, or to specified functionals thereof. DIMON is based on transporting a given problem (initial/boundary conditions and domain $Omega_theta$) to a problem on a reference domain $Omega_0$, where training data from multiple problems is used to learn the map to the solution on $Omega_0$, which is then re-mapped to the original domain $Omega_theta$. We consider several problems to demonstrate the performance of the framework in learning both static and time-dependent PDEs on non-rigid geometries; these include solving the Laplace equation, reaction-diffusion equations, and a multiscale PDE that characterizes the electrical propagation on the left ventricle. This work paves the way toward the fast prediction of PDE solutions on a family of domains and the application of neural operators in engineering and precision medicine.},

keywords = {digital twins, Machine learning, model reduction, 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 = {2023-06-13},

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

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 = {digital twins, 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{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{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{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{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{BM:MMDPs,

title = {Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning},

author = {Jake Bouvrie and Mauro Maggioni},

url = {http://arxiv.org/abs/1212.1143},

year  = {2012},

date = {2012-01-01},

keywords = {Machine learning, multiscale analysis, reinforcement learning, representation learning, spectral graph theory, transfer 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{FFT2011,

title = {Multi-Resolution Geometric Analysis for data in high dimensions},

author = {Guangliang Chen and Anna V Little and Mauro Maggioni},

year  = {2011},

date = {2011-08-01},

journal = {Proc. FFT 2011},

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

pubstate = {published},

tppubtype = {article}

}

@article{MM:Spars11talk,

title = {Multiscale Geometric Dictionaries for Point-Cloud Data, Presented at SPARS 11, http://www.math.duke.edu/~mauro/research.html#Talks},

author = {Mauro Maggioni},

url = {http://www.math.duke.edu/~mauro/research.html#Talks},

year  = {2011},

date = {2011-06-01},

note = {Presented at SPARS 11},

keywords = {dictionary learning, geometric wavelets, Machine learning, Manifold Learning, multiscale analysis},

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}

}