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

Giosue Migliorini, Padhraic Smyth
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:3484-3492, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-migliorini26a, title = { Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space }, author = {Migliorini, Giosue and Smyth, Padhraic}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {3484--3492}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/migliorini26a/migliorini26a.pdf}, url = {https://proceedings.mlr.press/v300/migliorini26a.html}, 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. } }
Endnote
%0 Conference Paper %T Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space %A Giosue Migliorini %A Padhraic Smyth %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-migliorini26a %I PMLR %P 3484--3492 %U https://proceedings.mlr.press/v300/migliorini26a.html %V 300 %X 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.
APA
Migliorini, G. & Smyth, P.. (2026). Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:3484-3492 Available from https://proceedings.mlr.press/v300/migliorini26a.html.

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