Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems

Lukas Köhs, Bastian Alt, Heinz Koeppl
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:11430-11454, 2022.

Abstract

Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equations models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-kohs22a, title = {{M}arkov Chain {M}onte {C}arlo for Continuous-Time Switching Dynamical Systems}, author = {K{\"o}hs, Lukas and Alt, Bastian and Koeppl, Heinz}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {11430--11454}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/kohs22a/kohs22a.pdf}, url = {https://proceedings.mlr.press/v162/kohs22a.html}, abstract = {Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equations models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.} }
Endnote
%0 Conference Paper %T Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems %A Lukas Köhs %A Bastian Alt %A Heinz Koeppl %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-kohs22a %I PMLR %P 11430--11454 %U https://proceedings.mlr.press/v162/kohs22a.html %V 162 %X Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equations models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.
APA
Köhs, L., Alt, B. & Koeppl, H.. (2022). Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:11430-11454 Available from https://proceedings.mlr.press/v162/kohs22a.html.

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