Online EM Algorithm for Hidden Markov Models
Résumé
This paper is about the estimation of fixed model parameters in hidden Markov models using an online (or recursive) version of the Expectation-Maximization (EM) algorithm. It is first shown that under suitable mixing assumptions, the large sample behavior of the traditional (batch) EM algorithm may be analyzed through the notion of a limiting EM recursion, which is deterministic. This observation generalizes results previously obtained for latent data model with independent observations. By using the recursive implementation of smoothing computations associated with sum functionals of the hidden state, it is then possible to propose an online EM algorithm that generalizes an approach recently proposed in the case of HMMs with finite-valued observations. The performance of the proposed algorithm is numerically evaluated through simulations in the case of a noisily observed Markov chain.
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