Tree augmented naive Bayes for regression using mixtures of truncated exponentials: application to higher education management

Authors:
Antonio Fernández;María Morales;Antonio Salmerón
Affiliations:
Department of Statistics and Applied Mathematics, University of Almería, Almería, Spain;Department of Statistics and Applied Mathematics, University of Almería, Almería, Spain;Department of Statistics and Applied Mathematics, University of Almería, Almería, Spain
Venue:
IDA'07 Proceedings of the 7th international conference on Intelligent data analysis
Year:
2007

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Abstract

In this paper we explore the use of Tree Augmented Naive Bayes (TAN) in regression problems where some of the independent variables are continuous and some others are discrete. The proposed solution is based on the approximation of the joint distribution by a Mixture of Truncated Exponentials (MTE). The construction of the TAN structure requires the use of the conditional mutual information, which cannot be analytically obtained for MTEs. In order to solve this problem, we introduce an unbiased estimator of the conditional mutual information, based on Monte Carlo estimation. We test the performance of the proposed model in a real life context, related to higher education management, where regression problems with discrete and continuous variables are common.