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

The paper introduces Optimized Conformal Selection (OptCS), a framework that enables valid multiple testing after flexible, data‑driven construction of conformity scores. OptCS allows the use of all labeled data for score training and handles complex p‑value dependencies to maintain finite‑sample false discovery rate control. Three specific procedures are proposed: selecting a powerful score among candidates, training the score with all labeled data without sample splitting, and combining full‑sample training with model selection, with effectiveness demonstrated in simulations and real drug‑discovery and language‑model applications.

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