Testing for outliers with conformal p-values
Stephen Bates, Emmanuel Candès, Lihua Lei, Yaniv Romano, Matteo Sesia
The Annals of Statistics · 2023 · Volume 51 · Issue 1
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.
Keywords
62G10, 62G15, 62J15, conformal inference, False discovery rate, out-of-distribution, Positive dependence
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