Optimality of kernel density estimation of prior distribution in bayes network

Authors:
Hengqing Tong;Yanfang Deng;Ziling Li
Affiliations:
Department of Mathematics, Wuhan University of Technology, Wuhan, Hubei, China;Department of Mathematics, Wuhan University of Technology, Wuhan, Hubei, China;Department of Mathematics, Wuhan University of Technology, Wuhan, Hubei, China
Venue:
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Year:
2006

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Abstract

The key problem of inductive-learning in Bayes network is the estimator of prior distribution. This paper adopts general naive Bayes to handle continuous variables, and proposes a kind of kernel function constructed by orthogonal polynomials, which is used to estimate the density function of prior distribution in Bayes network. The paper then makes further researches into optimality of the kernel estimation of density and derivatives. When the sample is fixed, the estimators can keep continuity and smoothness, and when the sample size tends to infinity, the estimators can keep good convergence rates.