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State sequence prediction in imprecise hidden Markov models

Jasper De Bock UGent and Gert De Cooman UGent (2011) ISIPTA '11 - PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS. p.159-168
abstract
We present an efficient exact algorithm for estimating state sequences from outputs (or observations) in imprecise hidden Markov models (iHMM), where both the uncertainty linking one state to the next, and that linking a state to its output, are represented using coherent lower previsions. The notion of independence we associate with the credal network representing the iHMM is that of epistemic irrelevance. We consider as best estimates for state sequences the (Walley-Sen) maximal sequences for the posterior joint state model (conditioned on the observed output sequence), associated with a gain function that is the indicator of the state sequence. This corresponds to (and generalises) finding the state sequence with the highest posterior probability in HMMs with precise transition and output probabilities (pHMMs). We argue that the computational complexity is at worst quadratic in the length of the Markov chain, cubic in the number of states, and essentially linear in the number of maximal state sequences. For binary iHMMs, we investigate experimentally how the number of maximal state sequences depends on the model parameters.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
credal network, epistemic irrelevance, coherent lower prevision, maximality, optimal state sequence, Imprecise hidden Markov model
in
ISIPTA '11 - PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS
editor
F Coolen, G DeCooman, T Fetz and M Oberguggenberger
pages
159 - 168
conference name
7th International symposium on Imprecise Probability: Theories and Applications (ISIPTA 2011)
conference location
Innsbruck, Austria
conference start
2011-07-25
conference end
2011-07-28
Web of Science type
Proceedings Paper
Web of Science id
000323983600019
ISBN
9783902652409
project
Bioinformatics: from nucleotids to networks (N2N)
language
English
UGent publication?
yes
classification
P1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1978382
handle
http://hdl.handle.net/1854/LU-1978382
date created
2012-01-04 15:59:41
date last changed
2013-12-20 11:33:52
@inproceedings{1978382,
  abstract     = {We present an efficient exact algorithm for estimating state sequences from outputs (or observations) in imprecise hidden Markov models (iHMM), where both the uncertainty linking one state to the next, and that linking a state to its output, are represented using coherent lower previsions. The notion of independence we associate with the credal network representing the iHMM is that of epistemic irrelevance. We consider as best estimates for state sequences the (Walley-Sen) maximal sequences for the posterior joint state model (conditioned on the observed output sequence), associated with a gain function that is the indicator of the state sequence. This corresponds to (and generalises) finding the state sequence with the highest posterior probability in HMMs with precise transition and output probabilities (pHMMs). We argue that the computational complexity is at worst quadratic in the length of the Markov chain, cubic in the number of states, and essentially linear in the number of maximal state sequences. For binary iHMMs, we investigate experimentally how the number of maximal state sequences depends on the model parameters.},
  author       = {De Bock, Jasper and De Cooman, Gert},
  booktitle    = {ISIPTA '11 - PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS},
  editor       = {Coolen, F and DeCooman, G and Fetz, T and Oberguggenberger, M},
  isbn         = {9783902652409},
  keyword      = {credal network,epistemic irrelevance,coherent lower prevision,maximality,optimal state sequence,Imprecise hidden Markov model},
  language     = {eng},
  location     = {Innsbruck, Austria},
  pages        = {159--168},
  title        = {State sequence prediction in imprecise hidden Markov models},
  year         = {2011},
}

Chicago
De Bock, Jasper, and Gert De Cooman. 2011. “State Sequence Prediction in Imprecise Hidden Markov Models.” In ISIPTA  ’11 - PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS, ed. F Coolen, G DeCooman, T Fetz, and M Oberguggenberger, 159–168.
APA
De Bock, Jasper, & De Cooman, G. (2011). State sequence prediction in imprecise hidden Markov models. In F. Coolen, G. DeCooman, T. Fetz, & M. Oberguggenberger (Eds.), ISIPTA  ’11 - PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS (pp. 159–168). Presented at the 7th International symposium on Imprecise Probability: Theories and Applications (ISIPTA 2011).
Vancouver
1.
De Bock J, De Cooman G. State sequence prediction in imprecise hidden Markov models. In: Coolen F, DeCooman G, Fetz T, Oberguggenberger M, editors. ISIPTA  ’11 - PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS. 2011. p. 159–68.
MLA
De Bock, Jasper, and Gert De Cooman. “State Sequence Prediction in Imprecise Hidden Markov Models.” ISIPTA  ’11 - PROCEEDINGS OF THE SEVENTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS. Ed. F Coolen et al. 2011. 159–168. Print.