PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Sensitivity analysis in HMMs with application to likelihood maximization
Coquelin Pierre-Arnaud, Deguest Romain and Rémi Munos
NIPS 2009 2009.

Abstract

This paper considers a sensitivity analysis in Hidden Markov Models with con- tinuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the fil- tering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptoti- cally unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations. We derive an IPA estimator for the gradient of the log-likelihood, which may be used in a gradient method for the purpose of likelihood maximization. We illustrate the method with several numerical experiments.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:6113
Deposited By:Rémi Munos
Deposited On:08 March 2010