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

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Rezaei Tabar Vahid; Plewczynski Dariusz; Fathipour Hosna

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Journal: Journal of the Iranian Statistical Society Year:2018 | Volume:17 | Issue:2 Page(s): 205-225

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Title

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

Author(s)

Rezaei Tabar Vahid | Plewczynski Dariusz | Fathipour Hosna | Issue Writer Certificate

Keywords

Baum-Welch Algorithm

Bayesian Network

Hidden Markov Model

Viterbi Algorithm

Abstract

The parameters of a Hidden Markov Model (HMM) are transition and emis-sion 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 andViterbi Algorithms significantly outperform the conventional ones when sample sizes become larger.

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APA: Copy

Rezaei Tabar, Vahid, Plewczynski, Dariusz, & Fathipour, Hosna. (2018). Generalized Baum-Welch and Viterbi Algorithms Based on the Direct Dependency among Observations. JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS), 17(2), 205-225. SID. https://sid.ir/paper/747812/en

Vancouver: Copy

Rezaei Tabar Vahid, Plewczynski Dariusz, Fathipour Hosna. Generalized Baum-Welch and Viterbi Algorithms Based on the Direct Dependency among Observations. JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS)[Internet]. 2018;17(2):205-225. Available from: https://sid.ir/paper/747812/en

IEEE: Copy

Vahid Rezaei Tabar, Dariusz Plewczynski, and Hosna Fathipour, “Generalized Baum-Welch and Viterbi Algorithms Based on the Direct Dependency among Observations,” JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS), vol. 17, no. 2, pp. 205–225, 2018, [Online]. Available: https://sid.ir/paper/747812/en

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