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• W3156397721 abstract "This paper studies the construction of p-values for nonparametric outlier detection, from a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are outliers. We propose a solution based on conformal inference, a general framework yielding p-values that are marginally valid but mutually dependent for different test points. We prove these p-values are positively dependent and enable exact false discovery rate control, although in a relatively weak marginal sense. We then introduce a new method to compute p-values that are valid conditionally on the training data and independent of each other for different test points; this paves the way to stronger type-I error guarantees. Our results depart from classical conformal inference as we leverage concentration inequalities rather than combinatorial arguments to establish our finite-sample guarantees. Further, our techniques also yield a uniform confidence bound for the false positive rate of any outlier detection algorithm, as a function of the threshold applied to its raw statistics. Finally, the relevance of our results is demonstrated by experiments on real and simulated data." @default.
• W3156397721 created "2021-04-26" @default.
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• W3156397721 date "2023-02-01" @default.
• W3156397721 modified "2023-09-30" @default.
• W3156397721 title "Testing for outliers with conformal p-values" @default.
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• W3156397721 doi "https://doi.org/10.1214/22-aos2244" @default.
• W3156397721 hasPublicationYear "2023" @default.
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