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Article: Derivatives of entropy rate in special families of hidden Markov chains

TitleDerivatives of entropy rate in special families of hidden Markov chains
Authors
KeywordsAnalyticity
Entropy
Entropy rate
Hidden Markov chain
Hidden Markov model
Hidden Markov process
Issue Date2007
PublisherIEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?puNumber=18
Citation
Ieee Transactions On Information Theory, 2007, v. 53 n. 7, p. 2642-2652 How to Cite?
AbstractConsider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Recently Zuk etal showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise. Namely, they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time. We generalize this result to a natural class of hidden Markov chains called "Black Holes."We also discuss in depth special cases of binary Markov chains observed in binary-symmetric noise, and give an abstract formula for the first derivative in terms of a measure on the simplex due to Blackwell. © 2007 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/135158
ISSN
2015 Impact Factor: 1.737
2015 SCImago Journal Rankings: 1.433
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorHan, Gen_HK
dc.contributor.authorMarcus, Ben_HK
dc.date.accessioned2011-07-27T01:29:09Z-
dc.date.available2011-07-27T01:29:09Z-
dc.date.issued2007en_HK
dc.identifier.citationIeee Transactions On Information Theory, 2007, v. 53 n. 7, p. 2642-2652en_HK
dc.identifier.issn0018-9448en_HK
dc.identifier.urihttp://hdl.handle.net/10722/135158-
dc.description.abstractConsider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Recently Zuk etal showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise. Namely, they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time. We generalize this result to a natural class of hidden Markov chains called "Black Holes."We also discuss in depth special cases of binary Markov chains observed in binary-symmetric noise, and give an abstract formula for the first derivative in terms of a measure on the simplex due to Blackwell. © 2007 IEEE.en_HK
dc.languageengen_US
dc.publisherIEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?puNumber=18en_HK
dc.relation.ispartofIEEE Transactions on Information Theoryen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsIEEE Transactions on Information Theory. Copyright © IEEE.-
dc.rights©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.-
dc.subjectAnalyticityen_HK
dc.subjectEntropyen_HK
dc.subjectEntropy rateen_HK
dc.subjectHidden Markov chainen_HK
dc.subjectHidden Markov modelen_HK
dc.subjectHidden Markov processen_HK
dc.titleDerivatives of entropy rate in special families of hidden Markov chainsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0018-9448&volume=53&issue=7&spage=2642&epage=2652&date=2007&atitle=Derivatives+of+Entropy+Rate+in+Special+Familes+of+Hidden+Markov+Chains-
dc.identifier.emailHan, G:ghan@hku.hken_HK
dc.identifier.authorityHan, G=rp00702en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1109/TIT.2007.899467en_HK
dc.identifier.scopuseid_2-s2.0-34447315277en_HK
dc.identifier.hkuros187919en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-34447315277&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume53en_HK
dc.identifier.issue7en_HK
dc.identifier.spage2642en_HK
dc.identifier.epage2652en_HK
dc.identifier.isiWOS:000247606300027-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridHan, G=8640067800en_HK
dc.identifier.scopusauthoridMarcus, B=7102086378en_HK

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