Transductive conformal inference with adaptive scores

Ulysse Gazin; Gilles Blanchard; Etienne Roquain

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arXiv · 2310.18108

Transductive conformal inference with adaptive scores

Ulysse Gazin·Gilles Blanchard·Etienne Roquain

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Abstract

Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks. We consider the transductive setting, where decisions are made on a test sample of $m$ new points, giving rise to $m$ conformal $p$-values. While classical results only concern their marginal distribution, we show that their joint distribution follows a P\'olya urn model, and establish a concentration inequality for their empirical distribution function. The results hold for arbitrary exchangeable scores, including adaptive ones that can use the covariates of the test+calibration samples at training stage for increased accuracy. We demonstrate the usefulness of these theoretical results through uniform, in-probability guarantees for two machine learning tasks of current interest: interval prediction for transductive transfer learning and novelty detection based on two-class classification.

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Ulysse Gazin, Gilles Blanchard, Etienne Roquain. 2023-10-27. Transductive conformal inference with adaptive scores. https://arxiv.org/abs/2310.18108

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