Tree-based ranking methods

Stéphan Clémençon (1) , Nicolas Vayatis (2)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 CMLA - Centre de Mathématiques et de Leurs Applications

The paper investigates how recursive partitioning methods can be adapted to the bipartite ranking problem. In ranking, the pursued goal is global: based on past data, define an order on the whole input space X, so that positive instances take up the top ranks with maximum probability. The most natural way to order all instances consists of projecting the input data onto the real line through a real-valued scoring function s and use the natural order on R. The accuracy of the ordering induced by a candidate s is classically measured in terms of the ROC curve or the AUC. Here we discuss the design of tree-structured scoring functions obtained by recursively maximizing the AUC criterion. The connection with recursive piecewise linear approximation of the optimal $\roc$ curve both in the L1-sense and in the L{\infty}-sense is highlighted. A novel tree-based algorithm for ranking, called TreeRank, is proposed. Consistency results and generalization bounds of functional nature are established for this ranking method, when considering either the L1 or L{\infty} distance. We also describe committee-based learning procedures using TreeRank as a "base ranker", in order to overcome obvious drawbacks of such a top-down partitioning technique. Simulation results on artificial data are also displayed.

Mots clés: bipartite ranking; decision trees; pruning; ROC curve; AUC

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Stéphan Clémençon, Nicolas Vayatis. Tree-based ranking methods. 2008. ⟨hal-00268068v5⟩