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08/17/2023
Ensemble Kalman Filters with Resampling
Filtering is concerned with online estimation of the state of a dynamica...
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04/19/2023
Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators Under Mesh Refinement
This paper analyzes a popular computational framework to solve infinite-...
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01/27/2023
Reduced-Order Autodifferentiable Ensemble Kalman Filters
This paper introduces a computational framework to reconstruct and forec...
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10/20/2022
Optimization on Manifolds via Graph Gaussian Processes
This paper integrates manifold learning techniques within a Gaussian pro...
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08/05/2022
Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization
Many modern algorithms for inverse problems and data assimilation rely o...
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07/03/2022
Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning
In recent decades, science and engineering have been revolutionized by a...
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05/19/2022
Hierarchical Ensemble Kalman Methods with Sparsity-Promoting Generalized Gamma Hyperpriors
This paper introduces a computational framework to incorporate flexible ...
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11/26/2021
A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors
Hierarchical models with gamma hyperpriors provide a flexible, sparse-pr...
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09/06/2021
Finite Element Representations of Gaussian Processes: Balancing Numerical and Statistical Accuracy
The stochastic partial differential equation approach to Gaussian proces...
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07/16/2021
Auto-differentiable Ensemble Kalman Filters
Data assimilation is concerned with sequentially estimating a temporally...
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06/12/2021
Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries
This paper develops manifold learning techniques for the numerical solut...
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10/26/2020
Iterative Ensemble Kalman Methods: A Unified Perspective with Some New Variants
This paper provides a unified perspective of iterative ensemble Kalman m...
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09/22/2020
Bayesian Update with Importance Sampling: Required Sample Size
Importance sampling is used to approximate Bayes' rule in many computati...
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08/26/2020
Posterior Contraction Rates for Graph-Based Semi-Supervised Classification
This paper studies Bayesian nonparametric estimation of a binary regress...
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04/16/2020
The SPDE Approach to Matérn Fields: Graph Representations
This paper investigates Gaussian Markov random field approximations to n...
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03/18/2020
Data-Driven Forward Discretizations for Bayesian Inversion
This paper suggests a framework for the learning of discretizations of e...
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10/23/2019
Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds
This paper investigates the formulation and implementation of Bayesian i...
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04/06/2019
Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis
Several data analysis techniques employ similarity relationships between...
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01/29/2019
Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning
The aim of this paper is to provide new theoretical and computational un...
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08/09/2018
Spatial extreme values: variational techniques and stochastic integrals
This work employs variational techniques to revisit and expand the const...
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10/20/2017
On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms
A popular approach to semi-supervised learning proceeds by endowing the ...
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06/22/2017