Ensemble Hidden Markov Models with Extended Observation Densities for Biosignal Analysis

Abstract

Hidden Markov Models (HMM) have proven to be very useful in a variety of biomedical applications. The most established method for estimating HMM parameters is the maximum likelihood method which has shortcomings, such as repeated estimation and penalisation of the likelihood score, that are well known. This paper describes a variational learning approach to try and improve on the maximum-likelihood estimators. Emphasis lies on the fact that for HMMs with observation models that are from the exponential family of distributions, all HMM parameters and hidden state variables can be derived from a single loss function, namely the Kullback-Leibler divergence. Practical issues, such as model initialisation and choice of model order, are described. The paper concludes with application of three types of observation model HMMs to a variety of biomedical data, such as EEG and ECG, from different physiological experiments and conditions.