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Recursive estimation of multivariate hidden Markov model parameters

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Abstract

This article addresses a recursive parameter estimation algorithm for a hidden Markov model (HMM). The work focuses on an HMM with multiple states that are assumed to follow from a multivariate Gaussian distribution. The novelty of this study lies in a state transition probability calculation technique that simplifies the application of the backward stage of the forward–backward algorithm. For sequential observation analysis, the complexity of the created recursive algorithm for learning the HMM parameters is merely linear. Meanwhile, the classical Baum–Welch algorithm has second order complexity; therefore, it cannot be applied in online analysis situations. The properties of the proposed recursive expectation–maximization (EM) algorithm were explored by a computer simulation solving test examples and demonstrate that this algorithm can be efficiently applied to solve online tasks related to HMM parameter estimation.

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Authors and Affiliations

  1. Institute of Data Science and Digital Technologies, Vilnius University, Akademijos str. 4, 04812, Vilnius, Lithuania

    Jūratė Vaičiulytė

  2. Klaipėda University, H. Manto str. 84, 92294, Klaipėda, Lithuania

    Leonidas Sakalauskas

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  1. Jūratė Vaičiulytė
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  2. Leonidas Sakalauskas
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Correspondence to Jūratė Vaičiulytė.

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Vaičiulytė, J., Sakalauskas, L. Recursive estimation of multivariate hidden Markov model parameters. Comput Stat 34, 1337–1353 (2019). https://doi.org/10.1007/s00180-019-00877-z

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