Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space
This work addresses inference challenges for researchers in fields like epidemiology and environmental science, offering a novel method for handling high-dimensional coupled hidden Markov models, though it builds incrementally on existing approximation techniques.
The authors tackled the intractable inference problem in high-dimensional systems of interacting continuous-time Markov chains by introducing Latent Interacting Particle Systems, which parameterize generators and use estimated look-ahead functions in a twisted Sequential Monte Carlo scheme, achieving effective results on a latent SIRS model and a neural wildfire spread model trained on real data.
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.