Forward-Backward Latent State Inference for Hidden Continuous-Time semi-Markov Chains
This work addresses a limitation in Hidden semi-Markov Models for researchers and practitioners dealing with continuous-time data, though it appears incremental as it extends existing methods to a more general setting.
The authors tackled the problem of irregularly spaced discrete event data from continuous-time phenomena by generalizing non-sampling-based latent state inference to latent Continuous-Time semi-Markov Chains, introducing exact integral equations and scalable algorithms that can be efficiently solved with numerical methods.
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.