Ensemble Coupled Hidden Markov Models for Joint Characterisation of Dynamic Signals

How does one model data with the aid of labels, when the labels themselves are noisy, unreliable and have their own dynamics? How does one measure interactions between variables that are so different in their nature that a direct comparison using, say cross-correlations, is meaningless? In this paper these problems are approached using Coupled Hidden Markov Models which are estimated in the Variational Bayesian framework. Signals can be diverse since each chain has its own observation model. Signals can have their own dynamics and may temporally lag or lead one another by allowing linking edges in the network topology to be estimated and chosen according to the most probable posterior model. Integrated feature extraction and modelling is accomplished by providing the Markov models models with linear observations models. We derive Coupled Hidden Markov Models estimators, apply and compare them with sampling based approaches found in the literature.