Concentration inequalities for two-sample rank processes with application to bipartite ranking

Clémençon, Stephan; Limnios, Myrto; Vayatis, Nicolas

doi:10.1214/21-ejs1907

Cited by 2 publications

(21 citation statements)

References 34 publications

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“…We also emphasize that concentration properties of two-sample linear rank processes (i.e. collections of two-sample linear rank statistics) have recently been studied in Clémençon et al [2021], motivated by the interpretation of (2.4) as a scalar statistical summary of the ROC curve relative to the pair (H, G). Based on these results, an exponential tail probability bound for (2.4) is proved in the Appendix section (see Theorem 10 therein), which is used in the theoretical analysis carried out in section 3.…”

Section: The Univariate Case -Rank Tests and Roc Analysismentioning

confidence: 99%

“…see section 3 in Clémençon et al [2021]. In absence of any ambiguity about the pair (H, G) of univariate distributions considered, we write W φ for the sake of simplicity.…”

Section: The Univariate Case -Rank Tests and Roc Analysismentioning

confidence: 99%

“…j=1 I{s(Y j ) ≤ t} for t ∈ R. In Clémençon et al [2021] (see also Clémençon and Vayatis [2009a]), the performance of scoring rules s(z) maximizing alternative scalar criteria, of the form of two-sample linear rank statistics based on the univariate samples {s(X 1 ), . .…”

Section: Bipartite Ranking -The Rationale Behind Our Approachmentioning

confidence: 99%

“…Notice finally that a very preliminary version of the two-stage testing method, limited to AUC optimization and 'ranksum' test statistics, has been previously outlined in the conference paper Clémençon et al [2009]. The present article presents ranking-based tests and analyzes their performance in a much more general framework: building on recent results established in Clémençon et al [2021] a wider class of ranking-based tests are considered, a finite-sample analysis of their power is carried out here and more complete experimental results are presented.…”

Section: Introductionmentioning

confidence: 97%

“…By means of concentration results for two-sample linear rank processes (i.e. collections of two-sample linear rank statistics) recently established in Clémençon et al [2021], the (unbiased) twostage testing procedure is analyzed from a nonasymptotic perspective. For nonparametric classes of alternative hypotheses, we prove bounds for the type-I and II errors of tests based on a scoring function s(z) maximizing a statistical counterpart of a bipartite ranking performance criterion (summarizing the ROC curve) taking the form of a two-sample linear rank statistic.…”

Section: Introductionmentioning

confidence: 99%

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A Bipartite Ranking Approach to the Two-Sample Problem

Clémençon¹,

Limnios²,

Vayatis³

2023

Preprint

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The two-sample problem, which consists in testing whether independent samples on R d are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention, especially because the information acquisition processes at work in the Big Data era often involve various sources, poorly controlled, leading to datasets possibly exhibiting a strong sampling bias. While classic methods relying on the computation of a discrepancy measure between the empirical distributions face the curse of dimensionality, we develop an alternative approach based on statistical learning and extending rank tests, capable of detecting small departures from the null assumption in the univariate case when appropriately designed. Overcoming the lack of natural order on R d when d ≥ 2, it is implemented in two steps. Assigning to each of the samples a label (positive vs negative) and dividing them into two parts, a preorder on R d defined by a real-valued scoring function is learned by means of a bipartite ranking algorithm applied to the first part and a rank test is applied next to the scores of the remaining observations to detect possible differences in distribution. Because it learns how to project the data onto the real line nearly like (any monotone transform of) the likelihood ratio between the original multivariate distributions would do, the approach is not much affected by the dimensionality, ignoring ranking model bias issues, and preserves the advantages of univariate rank tests. Nonasymptotic error bounds are proved based on recent concentration results for two-sample linear rank-processes and an experimental study shows that the approach promoted surpasses alternative methods standing as natural competitors.

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Section: The Univariate Case -Rank Tests and Roc Analysismentioning

confidence: 99%

“…see section 3 in Clémençon et al [2021]. In absence of any ambiguity about the pair (H, G) of univariate distributions considered, we write W φ for the sake of simplicity.…”

Section: The Univariate Case -Rank Tests and Roc Analysismentioning

confidence: 99%

Section: Bipartite Ranking -The Rationale Behind Our Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Bipartite Ranking Approach to the Two-Sample Problem

Clémençon¹,

Limnios²,

Vayatis³

2023

Preprint

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Learning to rank anomalies: scalar performance criteria and maximization of rank statistics

Limnios,

Noiry,

Clémençon

2024

Mach Learn

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The ability to collect and store ever more massive data, unlabeled in many cases, has been accompanied by the need to process them efficiently in order to extract relevant information and possibly design solutions based on the latter. In various situations, the vast majority of the observations exhibit the same behavior, while a small proportion deviates from it. Detecting these outlier observations (or equivalently defined as anomalies) is now one of the major challenges for machine learning applications (e.g. fraud detection or predictive maintenance). We propose here a novel methodology for outlier/anomaly detection, by learning a scoring function defined on the feature space allowing for ranking the observations by degree of abnormality. The scoring function is built through maximization of an empirical performance criterion taking the form of a (two-sample) linear rank statistic. We show that bipartite ranking algorithms can thus be used to learn nearly optimal scoring function with provable theoretical guarantees. We illustrate our methodology with numerical experiments based on open access online code.

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Concentration inequalities for two-sample rank processes with application to bipartite ranking

Cited by 2 publications

References 34 publications

A Bipartite Ranking Approach to the Two-Sample Problem

A Bipartite Ranking Approach to the Two-Sample Problem

Learning to rank anomalies: scalar performance criteria and maximization of rank statistics

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