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Approximation of stationary processes by hidden Markov models

On the stability radii of continuous-time infinite Markov jump linear systems

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Approximation of stationary processes by hidden Markov models

Content Provider	Springer Nature Link
Author	Finesso, Lorenzo Grassi, Angela Spreij, Peter
Copyright Year	2010
Abstract	Stochastic realization is still an open problem for the class of hidden Markov models (HMM): given the law Q of an HMM find a finite parametric description of it. Fifty years after the introduction of HMMs, no computationally effective realization algorithm has been proposed. In this paper we direct our attention to an approximate version of the stochastic realization problem for HMMs. We aim at the realization of an HMM of assigned complexity (number of states of the underlying Markov chain) which best approximates, in Kullback Leibler divergence rate, a given stationary law Q. In the special case of Q being the law of an HMM this corresponds to solving the approximate realization problem for HMMs. In general there is no closed form expression of the Kullback Leibler divergence rate, therefore we replace it, as approximation criterion, with the informational divergence between the Hankel matrices of the processes. This not only has the advantage of being easy to compute, while providing a good approximation of the divergence rate, but also makes the problem amenable to the use of nonnegative matrix factorization (NMF) techniques. We propose a three step algorithm, based on the NMF, which realizes an optimal HMM. The viability of the algorithm as a practical tool is tested on a few examples of HMM order reduction.
Starting Page	1
Ending Page	22
Page Count	22
File Format	PDF
ISSN	09324194
Journal	Mathematics of Control, Signals, and Systems
Volume Number	22
Issue Number	1
e-ISSN	1435568X
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-07-11
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hidden Markov model Approximation Kullback–Leibler divergence Divergence rate Nonnegative matrix factorization Hankel matrix Systems Theory, Control Communications Engineering, Networks Control , Robotics, Mechatronics
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Signal Processing Control and Systems Engineering

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Approximation of stationary processes by Hidden Markov Models”, manuscript (2008)

Approximation of the i-divergence between stationary and hidden markov processes.

Rational approximations of spectral densities based on the Alpha divergence

Upper Bound Kullback–Leibler Divergence for Transient Hidden Markov Models

Quickest Change Detection and Kullback-Leibler Divergence for Two-State Hidden Markov Models

Upper and lower bounds for approximation of the Kullback-Leibler divergence between Hidden Markov models

Approximation of stationary processes by hidden Markov models

The Kullback-Leibler Divergence Rate between Markov Sources (2004)

Quickest change detection and Kullback-Leibler divergence for two-state hidden Markov models

Approximation of stationary processes by hidden Markov models

Similar Documents

Approximation of stationary processes by Hidden Markov Models”, manuscript (2008)

Approximation of the i-divergence between stationary and hidden markov processes.

Rational approximations of spectral densities based on the Alpha divergence

Upper Bound Kullback–Leibler Divergence for Transient Hidden Markov Models

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