Forward-Backward Latent State Inference for Hidden Continuous-Time semi-Markov Chains
Nicolai Engelmann, Heinz Koeppl
Abstract
Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show that non-sampling-based latent state inference used in HSMM's can be generalized to latent Continuous-Time semi-Markov Chains (CTSMC's). We formulate integro-differential forward and backward equations adjusted to the observation likelihood and introduce an exact integral equation for the Bayesian posterior marginals and a scalable Viterbi-type algorithm for posterior path estimates. The presented equations can be efficiently solved using well-known numerical methods. As a practical tool, variable-step HSMM's are introduced. We evaluate our approaches in latent state inference scenarios in comparison to classical HSMM's.
BibTeX
@inproceedings{
engelmann2022forwardbackward,
title={Forward-Backward Latent State Inference for Hidden Continuous-Time semi-Markov Chains},
author={Nicolai Engelmann and Heinz Koeppl},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=IRSyuxfYNb}
}