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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Jul 25, 2026stat.ML
Conformalized selection has been widely applied to select high-quality candidates from large datasets with rigorous uncertainty quantification, such as reliable labeling, drug discovery, and the alignment of large language models. Nevertheless, existing methods assume clean responses on calibration data, an assumption that rarely holds in practice. In this paper, we formulate the above tasks as selecting candidates with true predicted labels or with responses exceeding certain values. We demonstrate that existing conformal selection methods fail to control the false discovery rate (FDR) or suffer from severe power loss under contaminated calibration data. To that end, we propose Robust Conformalized Selection (RCS), a unified framework for selective classification with valid FDR control under general label contamination. The key insight of RCS lies in a novel statistical reduction: by separately conditioning on different classes, we translate the intractable label noise into a localized covariate shift problem, which then enables a covariate-adjusted empirical-Bayes-type estimate of the number of false selections. Statistical properties such as the asymptotic FDR control, power optimality, and robustness of RCS are established. We further develop an instantiation of RCS under randomized response model, and also apply RCS to the task of selecting candidates with large response values. Extensive experiments on both simulated and real-world datasets demonstrate the effectiveness of RCS.
Chengyao Yu, Hongxin Wei, Bingyi Jing
Apr 13, 2026cs.LG
Conformal selection (CS) uses calibration data to identify test inputs whose unobserved outcomes are likely to satisfy a pre-specified minimal quality requirement, while controlling the false discovery rate (FDR). Existing methods fix the target FDR level before observing data, which prevents the user from adapting the balance between number of selected test inputs and FDR to downstream needs and constraints based on the available data. For example, in genomics or neuroimaging, researchers often inspect the distribution of test statistics, and decide how aggressively to pursue candidates based on observed evidence strength and available follow-up resources. To address this limitation, we introduce post-hoc CS (PH-CS), which generates a path of candidate selection sets, each paired with a data-driven false discovery proportion (FDP) estimate. PH-CS lets the user select any operating point on this path by maximizing a user-specified utility, arbitrarily balancing selection size and FDR. Building on conformal e-variables and the e-Benjamini-Hochberg (e-BH) procedure, PH-CS is proved to provide a finite-sample post-hoc reliability guarantee whereby the ratio between estimated FDP level and true FDP is, on average, upper bounded by 1, so that the average estimated FDP is, to first order, a valid upper bound on the true FDR. PH-CS is extended to control quality defined in terms of a general risk. Experiments on synthetic and real-world datasets demonstrate that, unlike CS, PH-CS can consistently satisfy user-imposed utility constraints while producing reliable FDP estimates and maintaining competitive FDR control.
Meiyi Zhu, Osvaldo Simeone
Date pendingcs.LG
Conformal prediction is a useful and versatile alternative to model calibration in machine learning classification. It replaces single-class prediction with prediction sets, guaranteeing that the a priori probability of the prediction sets containing the true class is larger than or equal to a pre-specified rate. The size and usefulness of the prediction sets relies heavily on the choice of the non-conformity score function. The scientific literature contains many examples of non-conformity score functions but there is an absence of studies examining their properties and effectiveness. In this paper, we give an overview of properties of non-conformity score functions. We give examples of non-conformity score functions in the existing literature and introduce original modifications. We introduce an original method of evaluating the prediction set sizes of conformal predictors and use it to provide a comparison between non-conformity score functions. We also examine efficacy of different non-conformity score functions for class-conditional conformal prediction in a setting with imbalanced classes.
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