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

• URL: http://arxiv.org/abs/2510.12916v1
• Date: Tue, 14 Oct 2025 18:42:12 GMT
• Title: Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space
• Authors: Giosue Migliorini, Padhraic Smyth,
• Abstract summary: We introduce Latent Interacting Particle Systems, a model class parameterizing the generator of each Markov chain in the system.<n>We demonstrate the effectiveness of our approach on a challenging posterior inference task for a latent SIRS model on a graph, and on a neural model for wildfire spread dynamics trained on real data.
• Score: 13.537748779869615
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Latent Interacting Particle Systems, 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 on a neural model for wildfire spread dynamics trained on real data.

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