Variational Inference for Continuous-Time Switching Dynamical Systems

TL;DR

This paper introduces a novel continuous-time variational inference method for switching dynamical systems, combining Gaussian process approximation with Markov jump process inference to enable Bayesian state estimation and parameter learning.

Contribution

It presents a new variational inference algorithm for continuous-time switching systems, addressing computational intractability with a Gaussian process and Markov jump process integration.

Findings

Effective Bayesian latent state estimation across continuous time.

Successful parameter estimation via variational EM.

Validated on both synthetic and real-world data.

Abstract

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are naturally described in continuous time, we present a model based on an Markov jump process modulating a subordinated diffusion process. We provide the exact evolution equations for the prior and posterior marginal densities, the direct solutions of which are however computationally intractable. Therefore, we develop a new continuous-time variational inference algorithm, combining a Gaussian process approximation on the diffusion level with posterior inference for Markov jump processes. By minimizing the path-wise Kullback-Leibler divergence we obtain (i) Bayesian latent state estimates for arbitrary points on the real axis and (ii) point estimates of unknown system parameters, utilizing variational expectation maximization. We extensively evaluate our algorithm under the model assumption and for real-world examples.