Variable Selection for Naive Bayes Semisupervised Learning

Abstract

This article deals with a semisupervised learning based on naive Bayes assumption. A univariate Gaussian mixture density is used for continuous input variables whereas a histogram type density is adopted for discrete input variables. The EM algorithm is used for the computation of maximum likelihood estimators of parameters in the model when we fix the number of mixing components for each continuous input variable. We carry out a model selection for choosing a parsimonious model among various fitted models based on an information criterion. A common density method is proposed for the selection of significant input variables. Simulated and real datasets are used to illustrate the performance of the proposed method.

Keywords:

• BIC
• Common density
• Density estimation
• EM algorithm
• Model selection
• Naive Bayes
• Semisupervised learning
• Variable selection.

Mathematics Subject Classification:

• 62H40
• 91G40.

Acknowledgment

This article is a part of Byong–Jeong Choi’s Ph.D. dissertation at the Korea University. The research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (NRF-2010-0026432).