Expectation propagation for continuous time stochastic processes

TL;DR

This paper introduces a variational inference method for reconstructing posterior distributions over trajectories of diffusion and Markov jump processes from discrete observations, demonstrating efficiency and accuracy.

Contribution

It develops a novel variational approximation framework for inverse problems involving continuous-time stochastic processes, extending to Markov jump processes via the chemical Langevin equation.

Findings

Method is computationally efficient.

Provides accurate posterior approximations.

Applicable to diffusion and Markov jump processes.

Abstract

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference. We then show how the approximation can be extended to a wide class of discrete-state Markov jump pro- cesses by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems.