Related papers: An Optimal Transport Formulation of Bayes' Law for…

We study non-linear Bayesian inverse problems arising from semilinear partial differential equations (PDEs) that can be transformed into linear Bayesian inverse problems. We are then able to extend the early stopping for Ensemble…

Designing optimal Bayes filters for nonlinear non-Gaussian systems is a challenging task. The main difficulties are: 1) representing complex beliefs, 2) handling non-Gaussian noise, and 3) marginalizing past states. To address these…

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become…

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Legland etal. (2011) is extended to non-Gaussian state space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed,…

We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…

We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove…

This work introduces a new, distributed implementation of the Ensemble Kalman Filter (EnKF) that allows for non-sequential assimilation of large datasets in high-dimensional problems. The traditional EnKF algorithm is computationally…

We present two neural network approaches that approximate the solutions of static and dynamic…

We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…

We study a rather general class of optimal "ballistic" transport problems for matrix-valued measures. These problems naturally arise, in the spirit of \emph{Y. Brenier. Comm. Math. Phys. (2018) 364(2) 579-605}, from a certain dual…

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…

We propose a new type of the Ensemble Kalman Filter (EnKF), which uses the Fast Fourier Transform (FFT) for covariance estimation from a very small ensemble with automatic tapering, and for a fast computation of the analysis ensemble by…

We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…

Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…

Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…

Coverage control algorithms have traditionally focused on static target densities, where agents are deployed to optimally cover a fixed spatial distribution. However, many applications involve time-varying densities, including environmental…

This article is an exposition on some recent theoretical advances in learning latent structured models, with a primary focus on the fundamental roles that optimal transport distances play in the statistical theory. We aim at what may be the…

The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an…

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…