Optimized Conformal Selection: Powerful Selective Inference After Data-Dependent Score Construction

We study data-driven score construction in conformal selection, which uses conformal p-values and multiple testing to select "interesting" instances with large unobserved labels from a pool of unlabeled data, while controlling the FDR in finite sample. While existing solutions require the score function to be constructed independent of the calibration and test data, it is desirable to select or construct powerful conformity score in a data-driven manner and to leverage all labeled data for score training when presented with many score choices and limited labeled data. We propose Optimized Conformal Selection (OptCS), a general framework that allows valid multiple testing after flexible data-driven score construction. We introduce general conditions under which OptCS constructs valid conformal p-values despite substantial data reuse and handles complex p-value dependencies to maintain finite-sample FDR control. We instantiate this general recipe to propose three FDR-controlling procedures, each optimizing the models differently: (i) selecting a powerful score function among multiple candidates, (ii) training the score with all labeled data without sample splitting, and (iii) combining full-sample training and model selection. We demonstrate the efficacy of our methods via simulation studies and real applications in drug discovery and large language models.