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Article: Analyticity of entropy rate of hidden Markov chains
| Title | Analyticity of entropy rate of hidden Markov chains |
|---|---|
| Authors | |
| Keywords | Analyticity Entropy Entropy Rate Hidden Markov Chain Hidden Markov Process |
| Issue Date | 2006 |
| Publisher | IEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?puNumber=18 |
| Citation | IEEE Transactions On Information Theory, 2006, v. 52 n. 12, p. 5251-5266 How to Cite? |
| Abstract | We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions, the hidden Markov chain itself varies analytically, in a strong sense, as a function of the underlying Markov chain parameters. © 2006 IEEE. |
| Persistent Identifier | http://hdl.handle.net/10722/156183 |
| ISSN | 2023 Impact Factor: 2.2 2023 SCImago Journal Rankings: 1.607 |
| ISI Accession Number ID | |
| References |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Han, G | en_US |
| dc.contributor.author | Marcus, B | en_US |
| dc.date.accessioned | 2012-08-08T08:40:45Z | - |
| dc.date.available | 2012-08-08T08:40:45Z | - |
| dc.date.issued | 2006 | en_US |
| dc.identifier.citation | IEEE Transactions On Information Theory, 2006, v. 52 n. 12, p. 5251-5266 | en_US |
| dc.identifier.issn | 0018-9448 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10722/156183 | - |
| dc.description.abstract | We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions, the hidden Markov chain itself varies analytically, in a strong sense, as a function of the underlying Markov chain parameters. © 2006 IEEE. | en_US |
| dc.language | eng | en_US |
| dc.publisher | IEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?puNumber=18 | en_US |
| dc.relation.ispartof | IEEE Transactions on Information Theory | en_US |
| dc.rights | ©2006 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.subject | Analyticity | en_US |
| dc.subject | Entropy | en_US |
| dc.subject | Entropy Rate | en_US |
| dc.subject | Hidden Markov Chain | en_US |
| dc.subject | Hidden Markov Process | en_US |
| dc.title | Analyticity of entropy rate of hidden Markov chains | en_US |
| dc.type | Article | en_US |
| dc.identifier.email | Han, G:ghan@hku.hk | en_US |
| dc.identifier.authority | Han, G=rp00702 | en_US |
| dc.description.nature | published_or_final_version | en_US |
| dc.identifier.doi | 10.1109/TIT.2006.885481 | en_US |
| dc.identifier.scopus | eid_2-s2.0-33947364296 | en_US |
| dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-33947364296&selection=ref&src=s&origin=recordpage | en_US |
| dc.identifier.volume | 52 | en_US |
| dc.identifier.issue | 12 | en_US |
| dc.identifier.spage | 5251 | en_US |
| dc.identifier.epage | 5266 | en_US |
| dc.identifier.isi | WOS:000242503300005 | - |
| dc.publisher.place | United States | en_US |
| dc.identifier.scopusauthorid | Han, G=8640067800 | en_US |
| dc.identifier.scopusauthorid | Marcus, B=7102086378 | en_US |
| dc.identifier.issnl | 0018-9448 | - |