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April 2008 Ranking and Empirical Minimization of U-statistics
Stéphan Clémençon, Gábor Lugosi, Nicolas Vayatis
Ann. Statist. 36(2): 844-874 (April 2008). DOI: 10.1214/009052607000000910


The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn a ranking rule for deciding, among two instances, which one is “better,” with minimum ranking risk. Since the natural estimates of the risk are of the form of a U-statistic, results of the theory of U-processes are required for investigating the consistency of empirical risk minimizers. We establish, in particular, a tail inequality for degenerate U-processes, and apply it for showing that fast rates of convergence may be achieved under specific noise assumptions, just like in classification. Convex risk minimization methods are also studied.


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Stéphan Clémençon. Gábor Lugosi. Nicolas Vayatis. "Ranking and Empirical Minimization of U-statistics." Ann. Statist. 36 (2) 844 - 874, April 2008.


Published: April 2008
First available in Project Euclid: 13 March 2008

zbMATH: 1181.68160
MathSciNet: MR2396817
Digital Object Identifier: 10.1214/009052607000000910

Primary: 60C05, 60E15, 60G25, 68Q32

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 2 • April 2008
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