Entropy of hidden Markov processes and connections to dynamical systems : papers from the Banff International Research Station Workshop / edited by Brian Marcus, Karl Petersen, Tsachy Weissman.

Format:

Book

Contributor:

Marcus, Brian, 1949-

Petersen, Karl Endel, 1943-

Weissman, Tsachy.

Banff International Research Station for Mathematics Innovation & Discovery.

Series:

London Mathematical Society lecture note series ; 385.

London Mathematical Society lecture note series

Language:

English

Subjects (All):

Markov processes--Congresses.

Markov processes.

Entropy (Information theory)--Congresses.

Entropy (Information theory).

Dynamics--Congresses.

Dynamics.

Genre:

Conference papers and proceedings.

Physical Description:

vi, 272 pages : illustrations ; 23 cm.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2011.

Summary:

"Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterising the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is when mappings between dynamical systems map Markov measures to Markov (or Gibbs) measures or allow for Markov lifts of Markov chains"-- Provided by publisher.

Contents:

1 Hidden Markov processes in the context of symbolic dynamics / Mike Boyle, University of Maryland, College Park Park, Mike Boyle, University of Maryland, College, Karl Petersen, University of North Carolina, Chapel Hill Hill, Karl Petersen, University of North Carolina, Chapel 5

2 On the preservation of Gibbsianness under symbol amalgamation / Jean-René Chazottes, École Polytechnique, Palaisau Edgardo Ugalde, Universidad Autónoma de San Luis Potosí Potosí, Jean-René Chazottes, École Polytechnique, Palaisau Edgardo Ugalde, Universidad Autónoma de San Luis 72

3 A note on a complex Hilbert metric with application to domain of analyticity for entropy rate of hidden Markov processes / Guangyue Han, University of Hong Kong Kong, Guangyue Han, University of Hong, Brian Marcus, University of British Columbia Columbia, Brian Marcus, University of British, Yuval Peres, University of California at Berkeley Berkeley, Yuval Peres, University of California at 98

4 Bounds on the entropy rate of binary hidden Markov processes / Erik Ordentlich, Hewlett-Packard Laboratories Laboratories, Erik Ordentlich, Hewlett-Packard, Palo Alto Tsachy Weissman, Stanford University University, Palo Alto Tsachy Weissman, Stanford 117

5 Entropy rate for hidden Markov chains with rare transitions / Yuval Peres, Microsoft Research, Redmond Redmond, Yuval Peres, Microsoft Research,, Anthony Quas, University of Victoria, British Columbia Columbia, Anthony Quas, University of Victoria, British 172

6 The capacity of finite-state channels in the high-noise regime / Henry D. Pfister, Texas A&M University University, Henry D. Pfister, Texas A&M 179

7 Computing entropy rates for hidden Markov processes / Mark Pollicott, University of Warwick Warwick, Mark Pollicott, University of 223

8 Factors of Gibbs measures for full shifts / Mark Pollicott, University of Warwick Warwick, Mark Pollicott, University of, Thomas Kempton, University of Warwick Warwick, Thomas Kempton, University of 246

9 Thermodynamics of hidden Markov processes / Evgeny Verbitskiy, Leiden University and University of Groningen Groningen, Evgeny Verbitskiy, Leiden University and University of 258.

Notes:

Machine generated contents note: 1. Hidden Markov processes in the context of symbolic dynamics Mark Boyle and Karl Petersen; 2. On the preservation of Gibbsianess under symbol amalgamation Jean-Rene; Chazottes and E. Ugalde; 3. A note on a complex Hilbert metric with application to domain of analyticity for entropy rate of hidden Markov processes Guangyue Han, Brian Marcus and Yuval Peres; 4. Bounds on the entropy rate of binary hidden Markov processes Erik Ordentlich and Tsachy Weissman; 5. Entropy rate for hidden Markov chains with rare transitions Yuval Peres and Anthony Quas; 6. The capacity of finite-state channels in the high-noise regime Henry Pfister; 7. Computing entropy rates for hidden Markov processes Mark Pollicott; 8. Factors of Gibbs measures for full shifts Mark Pollicott and Thomas Kempton; 9. Thermodynamics of hidden Markov processes Evgeny Verbitskiy.

Includes bibliographical references.

ISBN:

0521111137

9780521111133

OCLC:

703205174

Online:

Cover image