Continuous-time Particle Filtering for Latent Stochastic Differential Equations

TL;DR

This paper introduces continuous-time particle filtering, extending traditional particle filtering to continuous-time stochastic processes, and demonstrates its superior performance in inference tasks involving neural stochastic differential equations.

Contribution

The authors develop a novel continuous latent particle filtering method that can replace variational inference techniques in continuous-time models.

Findings

Superior likelihood estimation performance

Enhanced sequential prediction accuracy

Effective inference across diverse stochastic processes

Abstract

Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior distribution of some stochastic process. In this work, we propose continuous latent particle filters, an approach that extends particle filtering to the continuous-time domain. We demonstrate how continuous latent particle filters can be used as a generic plug-in replacement for inference techniques relying on a learned variational posterior. Our experiments with different model families based on latent neural stochastic differential equations demonstrate superior performance of continuous-time particle filtering in inference tasks like likelihood estimation and sequential prediction for a variety of stochastic processes.