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Lipschitz Parametrization of Probabilistic Graphical Models
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@MISC{Honorio_lipschitzparametrization,
author = {Jean Honorio},
title = {Lipschitz Parametrization of Probabilistic Graphical Models},
year = {}
}
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Abstract
We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the ℓp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the Kullback-Leibler divergence that allows understanding methods that penalize the ℓp-norm of differences of parameters as the minimization of that upper bound. The expected log-likelihood is lower bounded by the negative ℓp-norm, which allows understanding the generalization ability of probabilistic models. The exponential of the negative ℓp-norm is involved in the lower bound of the Bayes error rate, which shows that it is reasonable to use parameters as features in algorithms that rely on metric spaces (e.g. classification, dimensionality reduction, clustering). Our results do not rely on specific algorithms for learning the structure or parameters. We show preliminary results for activity recognition and temporal segmentation. 1
Keyphrases
lipschitz parametrization probabilistic graphical model upper bound negative p-norm specific algorithm several implication several probabilistic graphical model probabilistic model activity recognition preliminary result bayes error rate generalization ability dimensionality reduction kullback-leibler divergence metric space temporal segmentation expected log-likelihood
