Partial Conjunction Conformal Selection

Conformal selection (CS) provides finite-sample guarantees for False Discovery Rate (FDR) control when selecting a subset of high-quality candidates from a large pool. Existing multivariate conformal selection (MCS) methods are restricted to the “all-or-nothing” rule (i.e., samples are selected only if all criteria are satisfied) and do not address the practical need for $r$-out-of-$d$ conjunction rules. In this study, we show that directly applying unadjusted partial conjunction combinations to componentwise conformal $p$-values can fail to preserve FDR control in the CS setting. To address this, we propose Partial Conjunction Conformal Selection (PCCS), a unified framework that accommodates both the global $r$-out-of-$d$ and block-level $r_0$-out-of-$L$ conjunction rules. In particular, we introduce two types of novel nonconformity scores to construct conformal $p$-values and then run the Benjamini–Hochberg (BH) procedure, thereby providing theoretical guarantees for finite-sample FDR control. Simulated and real-world experiments demonstrate that PCCS maintains valid FDR control while substantially improving selection power, establishing a versatile framework for selection tasks such as drug property prediction, LLM response filtering, and monocular depth estimation.