Recursive estimation of multivariate hidden Markov model parameters

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 techni...

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Bibliographic Details
Published in:Computational statistics Vol. 34; no. 3; pp. 1337 - 1353
Main Authors: Vaičiulytė, Jūratė, Sakalauskas, Leonidas
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019
Springer Nature B.V
Subjects:
Algorithms
Complexity
Computer simulation
Economic Theory/Quantitative Economics/Mathematical Methods
Machine learning
Markov analysis
Markov chains
Mathematics and Statistics
Normal distribution
Original Paper
Parameter estimation
Probability and Statistics in Computer Science
Probability Theory and Stochastic Processes
Statistical analysis
Statistics
Transition probabilities
Likelihood method
Clustering
Hidden Markov models
Recursive EM algorithm
ISSN:0943-4062, 1613-9658
Online Access:Get full text
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Summary: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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ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-019-00877-z