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Assistant Professor Department of Statistics, Faculty of mathematics and Computer Sciences, Allameh Tabataba'i University, Tehran, Iran.
Abstract:   (283 Views)

‎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 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 datasets which are related to biological and inflation data‎. ‎We show that the generalized Baum-Welch and Viterbi algorithms significantly outperform the conventional ones when the sample sizes become larger‎.

Type of Study: Original Paper | Subject: 60Jxx: Markov processes
Received: 2017/06/12 | Accepted: 2018/02/27 | Published: 2018/02/27