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Lumpable Hidden Markov Models - Model Reduction and Reduced Complexity Filtering

White, Langford; Mahony, Robert; Brushe, Gary

Description

This paper is concerned with filtering of hidden Markov processes (HMPs) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are...[Show more]

dc.contributor.authorWhite, Langford
dc.contributor.authorMahony, Robert
dc.contributor.authorBrushe, Gary
dc.date.accessioned2015-12-13T23:19:52Z
dc.date.available2015-12-13T23:19:52Z
dc.identifier.issn0018-9286
dc.identifier.urihttp://hdl.handle.net/1885/90461
dc.description.abstractThis paper is concerned with filtering of hidden Markov processes (HMPs) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are concerned. We prove necessary and sufficient conditions on the HMP for exact lumpability to hold. For a particular class of hidden Markov models (HMMs), namely finite output alphabet models, conditions for lumpability of all HMPs representable by a specified HMM are given. The corresponding optimal filter algorithms for the aggregated states are then derived. The paper also describes an approach to efficient suboptimal filtering for HMPs which are approximately lumpable. By this we mean that the HMM generating the process may be approximated by a lumpable HMM. This approach involves directly finding a lumped HMM which approximates the original HMM well, in a matrix norm sense. An alternative approach for model reduction based on approximating a given HMM by an exactly lumpable HMM is also derived. This method is based on the alternating convex projections algorithm. Some simulation examples are presented which illustrate the performance of the suboptimal filtering algorithms.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE Inc)
dc.sourceIEEE Transactions on Automatic Control
dc.subjectKeywords: Algorithms; Approximation theory; Computer simulation; Markov processes; Mathematical models; Matrix algebra; Lumpable hidden Markov models; Signal filtering and prediction
dc.titleLumpable Hidden Markov Models - Model Reduction and Reduced Complexity Filtering
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume45
dc.date.issued2000
local.identifier.absfor010203 - Calculus of Variations, Systems Theory and Control Theory
local.identifier.ariespublicationMigratedxPub20828
local.type.statusPublished Version
local.contributor.affiliationWhite, Langford, University of Adelaide
local.contributor.affiliationMahony, Robert, College of Engineering and Computer Science, ANU
local.contributor.affiliationBrushe, Gary, Commonwealth Department of Defence
local.bibliographicCitation.issue12
local.bibliographicCitation.startpage2297
local.bibliographicCitation.lastpage2306
local.identifier.doi10.1109/9.895565
dc.date.updated2015-12-12T09:01:15Z
local.identifier.scopusID2-s2.0-0034473838
CollectionsANU Research Publications

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