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04/26/2023
Kernel Methods are Competitive for Operator Learning
We present a general kernel-based framework for learning operators betwe...
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03/02/2023
Bayesian Posterior Perturbation Analysis with Integral Probability Metrics
In recent years, Bayesian inference in large-scale inverse problems foun...
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02/27/2023
An Approximation Theory Framework for Measure-Transport Sampling Algorithms
This article presents a general approximation-theoretic framework to ana...
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10/14/2022
A Kernel Approach for PDE Discovery and Operator Learning
This article presents a three-step framework for learning and solving pa...
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03/22/2022
An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms
This paper presents a variational representation of the Bayes' law using...
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07/25/2020
Posterior Consistency of Semi-Supervised Regression on Graphs
Graph-based semi-supervised regression (SSR) is the problem of estimatin...
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06/11/2020
Conditional Sampling With Monotone GANs
We present a new approach for sampling conditional measures that enables...
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05/07/2020
Model Reduction and Neural Networks for Parametric PDEs
We develop a general framework for data-driven approximation of input-ou...
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09/13/2019
Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
Graph Laplacians computed from weighted adjacency matrices are widely us...
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06/18/2019
Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods
Graph-based semi-supervised learning is the problem of propagating label...
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01/30/2019
Geometric structure of graph Laplacian embeddings
We analyze the spectral clustering procedure for identifying coarse stru...
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09/30/2018
Convergence and perturbation theory for an infinite-dimensional Metropolis-Hastings algorithm with self-decomposable priors
We study a Metropolis-Hastings algorithm for target measures that are ab...
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06/14/2018
Simultaneous model calibration and source inversion in atmospheric dispersion models
We present a cost-effective method for model calibration and solution of...
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04/20/2018