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

2025-10-14

AI Summary

This work addresses the challenge of posterior inference in high-dimensional continuous-time, discrete-state coupled hidden Markov models under noisy discrete observations—where exact inference is analytically intractable due to Doob’s *h*-transform. We propose an approximate inference framework based on an interacting particle system over latent variables. Our key contribution is a learnable forward-looking function parameterization that explicitly incorporates future observation information; combined with a twisted potential function and sequential Monte Carlo sampling, it yields efficient, low-variance posterior approximations. The method is validated on two complex systems: a graph-structured latent-variable SIRS epidemic model and a real-data-driven neural dynamical model of wildfire propagation. Results demonstrate substantial improvements in both inference accuracy and computational efficiency for high-dimensional continuous-time Markov chains under noisy observations.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Intractable inference in high-dimensional coupled Markov chains
• Approximating posterior processes with discrete noisy observations
• Estimating twist potentials for efficient sequential Monte Carlo

Innovation

• Parameterizes Markov chain generators in system
• Estimates look-ahead functions anticipating future information
• Uses twisted Sequential Monte Carlo sampling scheme