Learning Naïve Bayes Tree for Conditional Probability Estimation

Abstract

Naive Bayes Tree uses decision tree as the general structure and deploys naive Bayesian classifiers at leaves. The intuition is that naive Bayesian classifiers work better than decision trees when the sample data set is small. Therefore, after several attribute splits when constructing a decision tree, it is better to use naive Bayesian classifiers at the leaves than to continue splitting the attributes. In this paper, we propose a learning algorithm to improve the conditional probability estimation in the diagram of Naive Bayes Tree. The motivation for this work is that, for cost-sensitive learning where costs are associated with conditional probabilities, the score function is optimized when the estimates of conditional probabilities are accurate. The additional benefit is that both the classification accuracy and Area Under the Curve (AUC) could be improved. On a large suite of benchmark sample sets, our experiments show that the CLL tree outperforms the state-of-art learning algorithms, such as Naive Bayes Tree and naive Bayes significantly in yielding accurate conditional probability estimation and improving classification accuracy and AUC.