Approximation of the Optimal ROC Curve and a Tree-Based Ranking Algorithm

We consider the extension of standard decision tree methods to the bipartite rankingproblem. In ranking, the goal pursued is global: define an order on the whole input space in order to have positive instances on top with maximum probability. The most natural way of ordering all instances consists in projecting the input data xonto the real line using a real-valued scoring functionsand the accuracy of the ordering induced by a candidate sis classically measured in terms of the AUC. In the paper, we discuss the design of tree-structured scoring functions obtained by maximizing the AUC criterion. In particular, the connection with recursive piecewise linear approximation of the optimal ROC curve both in the L 1 -sense and in the L i¾? -sense is discussed.

[1]  László Györfi,et al.  A Probabilistic Theory of Pattern Recognition , 1996, Stochastic Modelling and Applied Probability.

[2]  Michael C. Mozer,et al.  Optimizing Classifier Performance via an Approximation to the Wilcoxon-Mann-Whitney Statistic , 2003, ICML.

[3]  Pedro M. Domingos,et al.  Tree Induction for Probability-Based Ranking , 2003, Machine Learning.

[4]  Gábor Lugosi,et al.  Ranking and Scoring Using Empirical Risk Minimization , 2005, COLT.

[5]  Dan Roth,et al.  Generalization Bounds for the Area Under the ROC Curve , 2005, J. Mach. Learn. Res..

[6]  Mehryar Mohri,et al.  AUC Optimization vs. Error Rate Minimization , 2003, NIPS.

[7]  中澤 真,et al.  Devroye, L., Gyorfi, L. and Lugosi, G. : A Probabilistic Theory of Pattern Recognition, Springer (1996). , 1997 .

[8]  Peter A. Flach,et al.  Learning Decision Trees Using the Area Under the ROC Curve , 2002, ICML.

[9]  James P. Egan,et al.  Signal detection theory and ROC analysis , 1975 .

[10]  Alain Rakotomamonjy,et al.  Optimizing Area Under Roc Curve with SVMs , 2004, ROCAI.

[11]  Jue Wang,et al.  An Effective Tree-Based Algorithm for Ordinal Regression , 2006, IEEE Intell. Informatics Bull..

[12]  Stéphan Clémençon,et al.  Tree-structured ranking rules and approximation of the optimal ROC curve , 2008 .

[13]  J. Hanley,et al.  The meaning and use of the area under a receiver operating characteristic (ROC) curve. , 1982, Radiology.

[14]  Yoram Singer,et al.  An Efficient Boosting Algorithm for Combining Preferences by , 2013 .

[15]  G. Lugosi,et al.  Ranking and empirical minimization of U-statistics , 2006, math/0603123.

[16]  Adam Krzyzak,et al.  A Distribution-Free Theory of Nonparametric Regression , 2002, Springer series in statistics.