Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911602296487936 |
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| author | Migliorini, Giosue Smyth, Padhraic |
| author_facet | Migliorini, Giosue Smyth, Padhraic |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space Migliorini, Giosue Smyth, Padhraic Machine Learning 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. |
| title | Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.12916 |