Bayesian Networks: a Non-Frequentist Approach for Parametrization, and a more Accurate Structural Complexity Measure

Sylvain Gelly 1 Olivier Teytaud 1
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7161
Abstract : The problem of calibrating relations from examples is a classical problem in learning theory. This problem has in particular been studied in the theory of empirical processes (providing asymptotic results), and through statistical learning theory. The application of learning theory to bayesian networks is still uncomplete and we propose a contribution, especially through the use of covering numbers. We deduce multiple corollaries, among which a non-frequentist approach for parameters learning and a score taking into account a measure of structural entropy that has never been taken into account before. We then investigate the algorithmic aspects of our theoretical solution, based on BFGS and adaptive refining of gradient calculus. Empirical results show the relevance of both the statistical results and the algorithmic solution.
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Revue des Sciences et Technologies de l'Information - Série RIA : Revue d'Intelligence Artificielle, Lavoisier, 2006
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Dernière modification le : jeudi 10 mai 2018 - 02:07:00
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Sylvain Gelly, Olivier Teytaud. Bayesian Networks: a Non-Frequentist Approach for Parametrization, and a more Accurate Structural Complexity Measure. Revue des Sciences et Technologies de l'Information - Série RIA : Revue d'Intelligence Artificielle, Lavoisier, 2006. 〈inria-00112838〉

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