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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
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Bioinformatics: from nucleotids to networks (N2N)
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.
Keywords
maximality, optimal state sequence, coherent lower prevision, epistemic irrelevance, credal network, Imprecise hidden Markov model

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Citation

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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.
@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},
  language     = {eng},
  location     = {Innsbruck, Austria},
  pages        = {159--168},
  title        = {State sequence prediction in imprecise hidden Markov models},
  year         = {2011},
}
Web of Science
Times cited: