Optimality of Kernel Density Estimation of Prior Distribution in Bayes Network

The key problem of inductive-learning in Bayes network is the estimator of prior distribution. This paper adopted general native Bayes to handle continuous variables, proposed a kind of kernel function constructed by orthogonal polynomials, which is used to estimate the density function of prior distribution in Bayes network. Paper then made further researches into optimality of kernel density estimation of density and derivatives. When the sample is fixed, the estimator can keep continuity and smoothness, and when size of a sample tends to infinity, the estimator can keep good convergence rates. 2