Related papers: Ensemble Transport Filter via Optimized Maximum Me…
We propose an Euler particle transport (EPT) approach for generative learning. The proposed approach is motivated by the problem of finding an optimal transport map from a reference distribution to a target distribution characterized by the…
We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown…
We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…
The ensemble Kalman filter is widely used in applications because, for high dimensional filtering problems, it has a robustness that is not shared for example by the particle filter; in particular it does not suffer from weight collapse.…
The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…
This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to…
In this paper, we propose a novel distributed algorithm for consensus optimization over networks and a robust extension tailored to deal with asynchronous agents and packet losses. Indeed, to robustly achieve dynamic consensus on the…
The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the…
This work proposes a mathematically founded mixed precision accumulation strategy for the inference of neural networks. Our strategy is based on a new componentwise forward error analysis that explains the propagation of errors in the…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…
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…
In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
Feedback particle filter (FPF) is a Monte-Carlo (MC) algorithm to approximate the solution of a stochastic filtering problem. In contrast to conventional particle filters, the Bayesian update step in FPF is implemented via a mean-field type…
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…
Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes as well as the uncertainty from physical sensors. In these settings, the Kalman filter and its ensemble version -…
Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient…