Bounds on Convergence of Entropy Rate Approximations in Hidden Markov Processes PDF Download
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Author: Nicholas F. Travers
Publisher:
ISBN: 9781303444012
Category :
Languages : en
Pages :
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Book Description
There is no general closed form expression for the entropy rate of a hidden Markov process. However, the finite length block estimates h(t) often converge to the true entropy rate h quite rapidly. We establish exponential bounds on the rate of convergence of the block estimates for finite hidden Markov models under several different conditions, including exactness, unifilarity, and a flag-state condition. In the case of unifilar hidden Markov models, we also give exponential bounds on the L1 and a.s. decay of the state uncertainty U(t).
Author: Nicholas F. Travers
Publisher:
ISBN: 9781303444012
Category :
Languages : en
Pages :
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Book Description
There is no general closed form expression for the entropy rate of a hidden Markov process. However, the finite length block estimates h(t) often converge to the true entropy rate h quite rapidly. We establish exponential bounds on the rate of convergence of the block estimates for finite hidden Markov models under several different conditions, including exactness, unifilarity, and a flag-state condition. In the case of unifilar hidden Markov models, we also give exponential bounds on the L1 and a.s. decay of the state uncertainty U(t).
Author: Katy Marchand
Publisher:
ISBN:
Category :
Languages : en
Pages : 148
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Book Description
Author: Brian Marcus
Publisher: Cambridge University Press
ISBN: 1139495747
Category : Mathematics
Languages : en
Pages : 279
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Book Description
This collection of research and survey papers sets out the theory of hidden Markov processes, in particular addressing a central problem of the subject: computation of the Shannon entropy rate of an HMP. Connections are drawn between approaches from various disciplines, whilst recent research results and open problems are described.
Author: Gareth O. Roberts
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 20
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Book Description
Author: Ravi R. Montenegro
Publisher: Now Publishers Inc
ISBN: 1933019298
Category : Computers
Languages : en
Pages : 133
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Book Description
Mathematical Aspects of Mixing Times in Markov Chains is a comprehensive, well-written review of the subject that will be of interest to researchers and students in computer and mathematical sciences.
Author: Olivier Cappé
Publisher: Springer Science & Business Media
ISBN: 0387289828
Category : Mathematics
Languages : en
Pages : 656
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Book Description
This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.
![Application of Geometric Bounds to Convergence Rates of Markov Chains and Markov Processes on R[superscript]n [microform] PDF](https://books.google.com/books/content/images/frontcover/Zz4IywAACAAJ?fife=w80-h100)
Author: Wai Kong Yuen
Publisher: National Library of Canada = Bibliothèque nationale du Canada
ISBN: 9780612586192
Category :
Languages : en
Pages : 188
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Book Description
![Application of Geometric Bounds to Convergence Rates of Markov Chains and Markov Processes on R[superscript]n PDF](https://books.google.com/books/content/images/frontcover/_AK_wwEACAAJ?fife=w80-h100)
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
![Application of Geometric Bounds to Convergence Rates of Markov Chains and Markov Processes on R[superscript]n PDF](https://books.google.com/books/content/images/frontcover/3u9BzwEACAAJ?fife=w80-h100)
Author: Wai Kong Yuen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Quantitative geometric rates of convergence for reversible Markov chains are closely related to the spectral gap of the corresponding operator, which is hard to calculate for general state spaces. This thesis describes a geometric argument to give different types of bounds for spectral gaps of Markov chains on bounded subsets of Rn and to compare the rates of convergence of different Markov chains. We also extend the discrete-time results to homogeneous continuous-time reversible Markov processes. The limit path bounds and the limit Cheeger's bounds are introduced. Two quantitative examples of 1-dimensional diffusions are studied for the limit Cheeger's bounds and a 'n'-dimensional diffusion is studied for the limit path bounds.
Author: Brian Marcus
Publisher:
ISBN: 9781139090063
Category :
Languages : en
Pages :
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Book Description
