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Inverse filtering for hidden Markov models
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0002-1927-1690
2017 (English)In: Advances in Neural Information Processing Systems, Neural information processing systems foundation , 2017, Vol. 2017, p. 4205-4214Conference paper, Published paper (Refereed)
Abstract [en]

This paper considers a number of related inverse filtering problems for hidden Markov models (HMMs). In particular, given a sequence of state posteriors and the system dynamics; i) estimate the corresponding sequence of observations, ii) estimate the observation likelihoods, and iii) jointly estimate the observation likelihoods and the observation sequence. We show how to avoid a computationally expensive mixed integer linear program (MILP) by exploiting the algebraic structure of the HMM filter using simple linear algebra operations, and provide conditions for when the quantities can be uniquely reconstructed. We also propose a solution to the more general case where the posteriors are noisily observed. Finally, the proposed inverse filtering algorithms are evaluated on real-world polysomnographic data used for automatic sleep segmentation.

Place, publisher, year, edition, pages
Neural information processing systems foundation , 2017. Vol. 2017, p. 4205-4214
Series
Advances in Neural Information Processing Systems, ISSN 1049-5258 ; 2017
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-228586Scopus ID: 2-s2.0-85047014120OAI: oai:DiVA.org:kth-228586DiVA, id: diva2:1210287
Conference
31st Annual Conference on Neural Information Processing Systems, NIPS 2017, 4 December 2017 through 9 December 2017
Note

QC 20180528

Available from: 2018-05-28 Created: 2018-05-28 Last updated: 2018-05-28Bibliographically approved

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Mattila, RobertWahlberg, Bo

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