Null-Calibrated Conformal Selection via Target-Membership Scores

• URL: http://arxiv.org/abs/2606.22336v1
• Date: Sun, 21 Jun 2026 05:03:04 GMT
• Title: Null-Calibrated Conformal Selection via Target-Membership Scores
• Abstract summary: Conformal selection aims to identify test candidates whose unknown responses fall in a target region while controlling the false discovery rate.<n>We argue that the natural score for selection is instead the target-membership probability.<n>We study membership-score-based conformal selection and isolate one conformal calibration route, Null-Calibrated Conformal Selection.
• Score: 0.6599344783327052
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conformal selection aims to identify test candidates whose unknown responses fall in a target region while controlling the false discovery rate. Existing methods often inherit prediction-oriented nonconformity scores, such as residual or clipped residual scores, from conformal prediction. We argue that the natural score for selection is instead the target-membership probability. This score directly addresses the binary event being selected, and any monotone transform of it gives the Neyman--Pearson oracle ranking at a fixed null selection level. This distinction is irrelevant for mean-monotone targets, where conventional scores induce essentially the same ranking, but becomes important for interval-valued, variance-driven, multimodal, or multi-condition targets, where prediction-oriented scores can be misaligned with selection power. We study membership-score-based conformal selection and isolate one conformal calibration route, Null-Calibrated Conformal Selection (NCCS), which ranks test scores against confirmed non-target calibration examples. Under null exchangeability, NCCS yields finite-sample valid null p-values, which can be combined with BY under arbitrary dependence or with BH under standard positive-dependence conditions. Experiments support the score principle: membership scores match conventional scores on mean-monotone targets, substantially improve over mean-score selection on variance-driven targets, and, when calibrated by NCCS, trade power for finite-sample null validity in rare-target regimes where direct empirical-FDP thresholding can be anti-conservative.

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