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.
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Bahl, L., Brown, P., de Souza, P., Mercer, R.: A tree-based statistical language model for natural language speech recognition. IEEE Transactions on Acoustics, Speech and Signal Processing 37, 1001–1008 (1989)
Bauer, E., Kohavi, R.: An empirical comparison of voting classification algorithms: Bagging, boosting and variants. Artificial Intelligence 36, 105–142 (1989)
Bradley, A.P.: The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recognition 30, 1145–1159 (1997)
Buntine, W.: Learning classification trees. In: Artificial Intelligence frontiers in statistics, pp. 182–201. Chapman & Hall, London (1993)
Ferri, C., Flach, P.A., Hernandez-Orallo, J.: Improving the AUC of Probabilistic Estimation Trees. In: Lavrač, N., Gamberger, D., Todorovski, L., Blockeel, H. (eds.) ECML 2003. LNCS, vol. 2837, pp. 121–132. Springer, Heidelberg (2003)
Hand, D.J., Till, R.J.: A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems. Machine Learning 45, 171–186 (2001)
Hastie, T., Pregibon, L.: Shrinking Trees. AT & T Bell Laboratories (1990)
Ling, C.X., Huang, J., Zhang, H.: AUC: a statistically consistent and more discriminating measure than accuracy. In: Proceedings of 18th International Conference on Artificial Intelligence (IJCAI 2003), pp. 329–341. Morgan Kaufmann, San Francisco (2003)
Ling, C.X., Yan, R.J.: Decision tree with Better Ranking. In: Proceedings of the Twentieth International Conference on Machine Learning (ICML 2003). AAAI Press, Menlo Park (2003)
McCallum, A., Rosenfeld, R., Mitchell, T., Ng, A.Y.: Improving text classification by shrinkage in a hierarchy of classes. In: Proceedings of the 15th International Conference on Machine Learning, pp. 359–367. Morgan Kaufmann, San Francisco (1998)
Pazzani, M., Merz, C., Murphy, P., Ali, K., Hume, T., Bunk, C.: Reducing misclassification costs. In: Proceedings of the Eleventh International Conference on Machine Learning, pp. 217–225. Morgan Kaufmann, San Francisco (1994)
Provost, F., Domingos, P.: Tree Induction for Probability-based Ranking. In: Machine Learning. Kluwer Academic Publishers, Dordrecht (2002)
Provost, F., Fawcett, T., Kohavi, R.: The case against accuracy estimation for comparing induction algorithms. In: Proceedings of the Fifteenth International Conference on Machine Learning, pp. 445–453. Morgan Kaufmann, San Francisco (1999)
Provost, F., Fawcett, T.: Analysis and visualization of classifier performance: Comparison under imprecise class and cost distributions. In: Proceedings of the Third International Conference on Knowledge Discovery and Data Mining (KDD 1997), pp. 43–48. AAAI Press, Menlo Park (1997)
Quinlan, J.R.: C4.5 Programs for Machine Learning. Morgan Kaufmann, San Mateo (1993)
Witten, I.H., Frank, E.: Data mining-practical machine learning tools and techniques with java implementation. Morgan Kaufmann, San Mateo (2000)
Zadrozny, B., Elkan, C.: Obtaining calibrated probability estimates from decision trees and Naive Bayesian classifiers. In: Proceedings of the 18th International Conference on Machine Learning, pp. 609–616. Morgan Kaufmann, San Francisco (2001)
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Wang, B., Zhang, H. (2006). Improving the Ranking Performance of Decision Trees. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds) Machine Learning: ECML 2006. ECML 2006. Lecture Notes in Computer Science(), vol 4212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11871842_44
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DOI: https://doi.org/10.1007/11871842_44
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