Refined learning of hidden Markov models with a modified Baum-Welch algorithm and informative components

Abstract

Methods for refined learning of hidden Markov models (HMMs) have been studied for decades, taking either structural or parametric perspectives. This paper discusses using informative components of state parameters to refine the training of HMMs. While the purpose of HMM learning is to decompose a high-dimensional observation space into latent states, we may still end up with high dimensional state models. A problem with such high dimensional state models is that if they are learned with limited amounts of training data, this will bias the likelihood during training, particularly when there are outliers in the observation sequence. We propose a modified Baum-Welch algorithm to estimate the HMM parameters over informative components selected with nearly sufficient statistics, using relative entropy tolerance. Our method produces a modified likelihood estimation in reduced dimensions, which decreases the computation complexity and preserves near-optimality of the HMM that is constructed. Two variations on the algorithm are discussed, one that deals with general state model and another that considers a special Gaussian case. The approach is evaluated with a problem of using pen tip trajectory for handwriting character verification and recognition. Two data sets are studied, one with low dimensionality and the other with high dimensionality. A comparison is performed of the results of using HMMs trained without and with informative state components. For both data sets, we found that our approach yields improvements in performance. The error rate varies with relative entropy change is also evaluated.