Time discretization of continuous-time filters and smoothers for HMM parameter estimation

Abstract : In this paper we propose algorithms for parameter estimation of fast-sampled homogeneous Markov chains observed in white Gaussian noise. Our algorithms are obtained by the robust discretization of stochastic differential equations involved in the estimation of continuous-time hidden Markov models (HMM's) via the EM algorithm. We present two algorithms: the first is based on the robust discretization of continuous-time filters that were recently obtained by Elliott to estimate quantities used in the EM algorithm; the second is based on the discretization of continuous-time smoothers, yielding essentially the well-known Baum-Welch re-estimation equations. The smoothing formulas for continuous-time HMM's are new, and their derivation involves two-sided stochastic integrals. The choice of discretization results in equations which are identical to those obtained by deriving the results directly in discrete time. The filter-based EM algorithm has negligible memory requirements; indeed, independent of the number of observations. In comparison the smoother-based discrete-time EM algorithm requires the use of the forward-backward algorithm, which is a fixed-interval smoothing algorithm and has memory requirements proportional to the number of observations. On the other hand, the computational complexity of the filter-based EM algorithm is greater than that of the smoother-based scheme. However, the filters may be suitable for parallel implementation. Using computer simulations we compare the smoother-based and filter-based EM algorithms for HMM estimation. We provide also estimates for the discretization error.
Type de document :
Article dans une revue
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 1996, IT--42 (2), pp.593--605. 〈10.1109/18.485727〉
Liste complète des métadonnées

https://hal.inria.fr/hal-00912052
Contributeur : Francois Le Gland <>
Soumis le : vendredi 20 décembre 2013 - 18:45:10
Dernière modification le : jeudi 11 janvier 2018 - 06:20:10

Identifiants

Collections

Citation

Matthew R. James, Vikram Krishnamurthy, François Le Gland. Time discretization of continuous-time filters and smoothers for HMM parameter estimation. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 1996, IT--42 (2), pp.593--605. 〈10.1109/18.485727〉. 〈hal-00912052〉

Partager

Métriques

Consultations de la notice

169