Semiparametric Bayesian networks for continuous data

Abstract

The Bayesian network is crucial for computer technology and artificial intelligence when dealing with probabilities. In this paper, we extended a new semiparametric model for Bayesian networks which is more flexible and robust than the parametric or linear one, providing a further generalization of the Gaussian Bayesian network. In the classical Gaussian Bayesian networks, the regression function between nodes has always been assumed to be linear. Actually, this is not necessary because the links between nodes may be more complex than simply linear relationships. Learning the structure of the semiparametric Bayesian network, by adding the nonlinear structures, was an important issue discussed in this work. We have illustrated the problem of estimating and testing both parameters and regression functions of the proposed model. We, then, introduced a new algorithm for constructing the proposed semiparametric Bayesian network. Some sensitivity analyses have been explained in order to validate the correctness of the network. Simulation studies and a real application for the energy field were used to examine the fitted model.

Keywords:

• Bayesian networks
• semiparametric regression model
• parents
• partially linear model
• kernel estimator