Improving the Ranking Performance of Decision Trees

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Abstract

An accurate ranking of instances based on their class probabilities, which is measured by AUC (area under the Receiver Operating Characteristics curve), is desired in many applications. In a traditional decision tree, two obstacles prevent it from yielding accurate rankings: one is that the sample size on a leaf is small, and the other is that the instances falling into the same leaf are assigned to the same class probability. In this paper, we propose two techniques to address these two issues. First, we use the statistical technique shrinkage which estimates the class probability of a test instance by using a linear interpolation of the local class probabilities on each node along the path from leaf to root. An efficient algorithm is also brought forward to learn the interpolating weights. Second, we introduce an instance-based method, the weighted probability estimation (WPE), to generate distinct local probability estimates for the test instances falling into the same leaf. The key idea is to assign different weights to training instances based on their similarities to the test instance in probability estimation. Furthermore, we combine shrinkage and WPE together to compensate for the defects of each. Our experiments show that both shrinkage and WPE improve the ranking performance of decision trees, and that their combination works even better. The experiments also indicate that various decision tree algorithms with the combination of shrinkage and WPE significantly outperform the original ones and other state-of-the-art techniques proposed to enhance the ranking performance of decision trees.