Towards Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space

NeurIPS 2025 Workshop FPI Submission64 Authors

Track: Main Track

Keywords: continuous time markov chains, latent variable models, hidden markov models, twisted smc, sequential monte carlo

TL;DR: We introduce an efficient twisted sequential Monte Carlo scheme for posterior inference of high dimensional, coupled hidden Markov models in continuous time and discrete state space.

Abstract:

Systems of interacting continuous time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete times, and incorporating it via a Doob's $h-$transform gives rise to an intractable posterior process that requires approximation. We introduce Hidden Interacting Particle Models (HIPMs), a model class parameterizing the generator of each Markov chain in the system.
Our inference method involves estimating look-ahead functions (twist potentials) that anticipate future information, for which we introduce an efficient parameterization. We incorporate this approximation in a twisted Sequential Monte Carlo sampling scheme. We demonstrate the effectiveness of our approach on a challenging posterior inference task for a latent SIRS model on a graph, and benchmark different methods to approximate the twist function.

Submission Number: 64