Learning interaction dynamics with coupled hidden Markov models

An analysis of interactions between different physiological control systems may only be possible with correlation functions if the signals have similar spectral distributions. Interactions between such signals can be modelled in state space rather than observation space, i.e. interactions are modelled after first translating the observations into a common domain. Coupled hidden Markov models (CHMM) are such state-space models. They form a natural extension to standard hidden Markov models. The authors perform CHMM parameter estimation under a Bayesian paradigm, using Gibbs sampling, and in a maximum likelihood framework, using the expectation maximisation algorithm. The performance differences between the estimators are demonstrated on simulated data as well as biomedical data. It is shown that the proposed method gives meaningful results when comparing two different signals, such as respiration and EEG