Subspace estimation and prediction methods for hidden Markov models
2009 (English)In: Annals of Statistics, ISSN 0090-5364, Vol. 37, no 6B, 4131-4152 p.Article in journal (Refereed) Published
Hidden Markov models (HMMs) are probabilistic functions of finite Markov chains, or, put in other words, state space models with finite state space. In this paper, we examine subspace estimation methods for HMMs whose output lies a finite set as well. In particular, we study the geometric structure arising from the nonminimality of the linear state space representation of HMMs, and consistency of a subspace algorithm arising from a certain factorization of the singular value decomposition of the estimated linear prediction matrix, For this algorithm, we show that the estimates of the transition and emission probability matrices are consistent up to a similarity transformation, and that the in-step linear predictor Computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear m-step predictor.
Place, publisher, year, edition, pages
2009. Vol. 37, no 6B, 4131-4152 p.
Hidden Markov model, linear innovation representation, prediction error representation, subspace estimation, consistency
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:kth:diva-61174DOI: 10.1214/09-AOS711ISI: 000271673700015OAI: oai:DiVA.org:kth-61174DiVA: diva2:478667
QC 2012011172012-01-162012-01-162012-01-17Bibliographically approved