Electronic Journal of Statistics

Online Expectation Maximization based algorithms for inference in Hidden Markov Models

Sylvain Le Corff and Gersende Fort

Full-text: Open access

Abstract

The Expectation Maximization (EM) algorithm is a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be available at each iteration of the algorithm. In this contribution, a new generic online EM algorithm for model parameter inference in general Hidden Markov Model is proposed. This new algorithm updates the parameter estimate after a block of observations is processed (online). The convergence of this new algorithm is established, and the rate of convergence is studied showing the impact of the block-size sequence. An averaging procedure is also proposed to improve the rate of convergence. Finally, practical illustrations are presented to highlight the performance of these algorithms in comparison to other online maximum likelihood procedures.

Article information

Source
Electron. J. Statist., Volume 7 (2013), 763-792.

Dates
Received: October 2012
First available in Project Euclid: 25 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1364220670

Digital Object Identifier
doi:10.1214/13-EJS789

Mathematical Reviews number (MathSciNet)
MR3040559

Zentralblatt MATH identifier
1336.62090

Subjects
Primary: 62L12: Sequential estimation 60J22: Computational methods in Markov chains [See also 65C40] 62F12: Asymptotic properties of estimators
Secondary: 65C60: Computational problems in statistics 62L20: Stochastic approximation

Citation

Le Corff, Sylvain; Fort, Gersende. Online Expectation Maximization based algorithms for inference in Hidden Markov Models. Electron. J. Statist. 7 (2013), 763--792. doi:10.1214/13-EJS789. https://projecteuclid.org/euclid.ejs/1364220670


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