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Sensitivity of hidden Markov models

Part of: Distribution theory - Probability Inference from stochastic processes Controllability, observability, and system structure Markov processes

Published online by Cambridge University Press:  14 July 2016

Alexander Yu. Mitrophanov ,
Alexandre Lomsadze  and
Mark Borodovsky
Alexander Yu. Mitrophanov*
Affiliation:
Georgia Institute of Technology
Alexandre Lomsadze*
Affiliation:
Georgia Institute of Technology
Mark Borodovsky*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: School of Biology, Georgia Institute of Technology, 310 Ferst Drive, Atlanta, GA 30332-0230, USA.
∗Postal address: School of Biology, Georgia Institute of Technology, 310 Ferst Drive, Atlanta, GA 30332-0230, USA.
∗∗Postal address: School of Biomedical Engineering, Georgia Institute of Technology, 313 Ferst Drive, Atlanta, GA 30332-0535, USA. Email address: mark@amber.biology.gatech.edu
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Abstract

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We derive a tight perturbation bound for hidden Markov models. Using this bound, we show that, in many cases, the distribution of a hidden Markov model is considerably more sensitive to perturbations in the emission probabilities than to perturbations in the transition probability matrix and the initial distribution of the underlying Markov chain. Our approach can also be used to assess the sensitivity of other stochastic models, such as mixture processes and semi-Markov processes.

Keywords

Hidden Markov modelMarkov chainmixturesemi-Markov processperturbation boundsensitivity analysis

MSC classification

Primary: 93B35: Sensitivity (robustness)
Secondary: 62M09: Non-Markovian processes 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60E05: Distributions
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 632 - 642
Copyright
© Applied Probability Trust 2005 

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