The article introduces Null-Calibrated Conformal Selection (NCCS), a method that utilizes target-membership probability scores to identify test candidates within a target region while controlling the false discovery rate. The authors argue that these membership scores provide a more natural ranking for selection tasks than conventional prediction-oriented nonconformity scores, particularly for complex targets. This distinction is critical for interval-valued, variance-driven, multimodal, or multi-condition targets where traditional scores may be misaligned with selection power. NCCS ranks test scores against confirmed non-target calibration examples to yield finite-sample valid null p-values under null exchangeability. These p-values can be combined with the Benjamini-Yekutieli procedure under arbitrary dependence or the Benjamini-Hochberg procedure under standard positive-dependence conditions. Experiments demonstrate that membership scores match conventional scores on mean-monotone targets but substantially improve performance on variance-driven targets. In rare-target regimes, NCCS trades power for finite-sample null validity, addressing issues where direct empirical-FDP thresholding can be anti-conservative.
Null-Calibrated Conformal Selection via Target-Membership Scores
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