Subspace estimation and prediction methods for hidden Markov models
(2009) In Annals of Statistics 37(6B). p.41314152 Abstract
 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 instep linear predictor Computed from the... (More)
 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 instep linear predictor Computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear mstep predictor. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1519679
 author
 Andersson, Sofia ^{LU} and Rydén, Tobias ^{LU}
 organization
 publishing date
 2009
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 consistency, subspace estimation, representation, prediction error, Hidden Markov model, linear innovation representation
 in
 Annals of Statistics
 volume
 37
 issue
 6B
 pages
 4131  4152
 publisher
 Institute of Mathematical Statistics
 external identifiers

 wos:000271673700015
 scopus:73949139622
 ISSN
 00905364
 DOI
 10.1214/09AOS711
 language
 English
 LU publication?
 yes
 id
 ffa1f2ee2daf4b3fad5e20e0f7aab751 (old id 1519679)
 date added to LUP
 20160401 14:53:06
 date last changed
 20210922 03:28:41
@article{ffa1f2ee2daf4b3fad5e20e0f7aab751, abstract = {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 instep linear predictor Computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear mstep predictor.}, author = {Andersson, Sofia and Rydén, Tobias}, issn = {00905364}, language = {eng}, number = {6B}, pages = {41314152}, publisher = {Institute of Mathematical Statistics}, series = {Annals of Statistics}, title = {Subspace estimation and prediction methods for hidden Markov models}, url = {http://dx.doi.org/10.1214/09AOS711}, doi = {10.1214/09AOS711}, volume = {37}, year = {2009}, }