Factored Filtering of Continuous-Time Systems

TL;DR

This paper introduces a factored filtering approach for continuous-time stochastic systems, using matrix exponential approximations via ODE integration and uniformization, with proven bounds and improved performance over existing methods.

Contribution

It presents a novel factored uniformization method for continuous-time filtering with theoretical KL-divergence bounds and empirical performance improvements.

Findings

Factored uniformization outperforms previous methods.

KL-divergence of filtering is bounded.

Experimental results confirm improved accuracy.

Abstract

We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and that the belief distribution is to be approximated as a product of marginals. The essential computation is the matrix exponential. We look at two different methods for its computation: ODE integration and uniformization of the Taylor expansion. For both we consider approximations in which only a factored belief state is maintained. For factored uniformization we demonstrate that the KL-divergence of the filtering is bounded. Our experimental results confirm our factored uniformization performs better than previously suggested uniformization methods and the mean field algorithm.