Variational Bayes for continuous hidden Markov models and its application to active learning

In this paper, we present a variational Bayes (VB) framework for learning continuous hidden Markov models (CHMMs), and we examine the VB framework within active learning. Unlike a maximum likelihood or maximum a posteriori training procedure, which yield a point estimate of the CHMM parameters, VB-based training yields an estimate of the full posterior of the model parameters. This is particularly important for small training sets since it gives a measure of confidence in the accuracy of the learned model. This is utilized within the context of active learning, for which we acquire labels for those feature vectors for which knowledge of the associated label would be most informative for reducing model-parameter uncertainty. Three active learning algorithms are considered in this paper: 1) query by committee (QBC), with the goal of selecting data for labeling that minimize the classification variance, 2) a maximum expected information gain method that seeks to label data with the goal of reducing the entropy of the model parameters, and 3) an error-reduction-based procedure that attempts to minimize classification error over the test data. The experimental results are presented for synthetic and measured data. We demonstrate that all of these active learning methods can significantly reduce the amount of required labeling, compared to random selection of samples for labeling.