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

Stéphan Clémençon; Myrto Limnios; Nicolas Vayatis

doi:10.1214/21-EJS1907

Article Dans Une Revue Electronic Journal of Statistics Année : 2021

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

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Stéphan Clémençon

Fonction : Auteur
PersonId : 174491
IdHAL : stephan-clemencon
ORCID : 0000-0002-5879-9500
IdRef : 08905203X

Signal, Statistique et Apprentissage

Département Images, Données, Signal

Myrto Limnios

Fonction : Auteur correspondant
PersonId : 745170
IdHAL : myrtolimnios
ORCID : 0000-0001-9365-4801
IdRef : 262149478

Connectez-vous pour contacter l'auteur

CB - Centre Borelli - UMR 9010

Nicolas Vayatis

Fonction : Auteur
PersonId : 830068

CB - Centre Borelli - UMR 9010

Résumé

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.

Domaines

Statistiques [math.ST] Théorie [stat.TH] Machine Learning [stat.ML]

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https://hal.science/hal-03190532

Soumis le : mardi 8 novembre 2022-10:43:08

Dernière modification le : mercredi 23 octobre 2024-10:30:04

Dates et versions

hal-03190532 , version 1 (06-04-2021)

hal-03190532 , version 2 (01-06-2022)

hal-03190532 , version 3 (08-11-2022)

Identifiants

HAL Id : hal-03190532 , version 3
ARXIV : 2104.02943
DOI : 10.1214/21-EJS1907

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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 , 2021, 15 (2), pp.4659 -- 4717. ⟨10.1214/21-EJS1907⟩. ⟨hal-03190532v3⟩

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

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