Generalized Baum-Welch and Viterbi Algorithms Based on the Direct Dependency among Observations

The parameters of a Hidden Markov Model (HMM) are transition and emission probabilities‎. ‎Both can be estimated using the Baum-Welch algorithm‎. ‎The process of discovering the sequence of hidden states‎, ‎given the sequence of observations‎, ‎is performed by the Viterbi algorithm‎. ‎In both Baum-Welch and Viterbi algorithms‎, ‎it is assumed that‎, ‎given the states‎, ‎the observations are independent from each other‎. ‎In this paper‎, ‎we first consider the direct dependency between consecutive observations in the HMM‎, ‎and then use conditional independence relations in the context of a Bayesian network which is a probabilistic graphical model for generalizing the Baum-Welch and Viterbi algorithms‎. ‎We compare the performance of the generalized algorithms with the commonly used ones in simulation studies for synthetic data‎. ‎We finally apply these algorithms on real data sets which are related to biological and inflation data‎. ‎We show that the generalized Baum-Welch and Viterbi algorithms significantly outperform the conventional ones when sample sizes become larger‎.