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Online expectation maximization based algorithms for inference in hidden Markov models. (English) Zbl 1336.62090
Summary: 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.

62F12 Asymptotic properties of parametric estimators
62L20 Stochastic approximation
62L12 Sequential estimation
60J22 Computational methods in Markov chains
65C60 Computational problems in statistics (MSC2010)
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