Variational Gaussian filtering via Wasserstein gradient flows

2023/03/11 by Adrien Corenflos, Corenflos, Adrien, Hany Abdulsamad +1 · 2 citations
Computer Science · #Anomaly Detection Techniques and Applications #Computation (stat.CO) #Computational Engineering #FOS: Computer and information sciences #FOS: Electrical engineering #Finance #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Systems and Control (eess.SY) #and Science (cs.CE) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2303.06398

openalex publication_date 2023/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy minimization on the space of probability distributions equipped with the Wasserstein metric. We outline the general method and show its competitiveness in posterior representation and parameter estimation on two state-space models for which Gaussian approximations typically fail: systems with multiplicative noise and multi-modal state distributions.

Cited by

• Recursive Entropic Variational Inference for Nonlinear State-Space Models
• A Recursive Theory of Variational State Estimation: The Dynamic Programming Approach

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