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Concentration Inequalities for Two-Sample Rank Processes with Application to Bipartite Ranking

Abstract : The ROC curve is the gold standard for measuring the performance of a test/scoring statistic regarding its capacity to discriminate between two statistical populations in a wide variety of applications, ranging from anomaly detection in signal processing to information retrieval, through medical diagnosis. Most practical performance measures used in scoring/ranking applications such as the AUC, the local AUC, the p-norm push, the DCG and others, can be viewed as summaries of the ROC curve. In this paper, the fact that most of these empirical criteria can be expressed as two-sample linear rank statistics is highlighted and concentration inequalities for collections of such random variables, referred to as two-sample rank processes here, are proved, when indexed by VC classes of scoring functions. Based on these nonasymptotic bounds, the generalization capacity of empirical maximizers of a wide class of ranking performance criteria is next investigated from a theoretical perspective. It is also supported by empirical evidence through convincing numerical experiments.
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https://hal.archives-ouvertes.fr/hal-03190532
Contributor : Myrto Limnios Connect in order to contact the contributor
Submitted on : Tuesday, April 6, 2021 - 1:13:09 PM
Last modification on : Tuesday, October 19, 2021 - 11:16:16 AM
Long-term archiving on: : Wednesday, July 7, 2021 - 6:33:49 PM

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  • HAL Id : hal-03190532, version 1
  • ARXIV : 2104.02943

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Stéphan Clémençon, Myrto Limnios, Nicolas Vayatis. Concentration Inequalities for Two-Sample Rank Processes with Application to Bipartite Ranking. Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2021, 15 (2), pp.4659 -- 4717. ⟨hal-03190532⟩

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