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Subspace estimation and prediction methods for hidden Markov models

Andersson, Sofia LU and Rydén, Tobias LU (2009) In Annals of Statistics 37(6B). p.4131-4152
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 in-step 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 in-step linear predictor Computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear m-step predictor. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
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
Inst Mathematical Statistics
external identifiers
  • wos:000271673700015
  • scopus:73949139622
ISSN
0090-5364
DOI
10.1214/09-AOS711
language
English
LU publication?
yes
id
ffa1f2ee-2daf-4b3f-ad5e-20e0f7aab751 (old id 1519679)
date added to LUP
2009-12-28 11:20:17
date last changed
2017-01-01 06:29:03
@article{ffa1f2ee-2daf-4b3f-ad5e-20e0f7aab751,
  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 in-step linear predictor Computed from the estimated system matrices is consistent, i.e., converges to the true optimal linear m-step predictor.},
  author       = {Andersson, Sofia and Rydén, Tobias},
  issn         = {0090-5364},
  keyword      = {consistency,subspace estimation,representation,prediction error,Hidden Markov model,linear innovation representation},
  language     = {eng},
  number       = {6B},
  pages        = {4131--4152},
  publisher    = {Inst Mathematical Statistics},
  series       = {Annals of Statistics},
  title        = {Subspace estimation and prediction methods for hidden Markov models},
  url          = {http://dx.doi.org/10.1214/09-AOS711},
  volume       = {37},
  year         = {2009},
}