Subspace estimation and prediction methods for hidden Markov models
(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:
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
- 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
- 2016-04-01 14:53:06
- date last changed
- 2022-01-28 02:59:00
@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}}, keywords = {{consistency; subspace estimation; representation; prediction error; Hidden Markov model; linear innovation representation}}, language = {{eng}}, number = {{6B}}, pages = {{4131--4152}}, publisher = {{Institute of Mathematical Statistics}}, series = {{Annals of Statistics}}, title = {{Subspace estimation and prediction methods for hidden Markov models}}, url = {{http://dx.doi.org/10.1214/09-AOS711}}, doi = {{10.1214/09-AOS711}}, volume = {{37}}, year = {{2009}}, }