Aggregating conformal prediction sets via 𝜶-allocation

Abstract Conformal prediction offers a distribution-free framework for constructing prediction sets with finite-sample coverage. Yet, efficiently leveraging multiple nonconformity scores to reduce set sizes remains an open challenge. Instead of selecting a single best score, this work introduces a principled aggregation strategy that intersects multiple conformal prediction sets whose confidence levels are optimally allocated to minimize empirical set size while maintaining asymptotic coverage. Two variants are developed to guarantee finite-sample coverage via sample splitting and full conformalization, respectively. An individualized allocation strategy is further proposed to promote local size efficiency while achieving asymptotic conditional coverage. Extensive experiments on synthetic and real-world datasets demonstrate that our approach achieves considerably smaller prediction sets than state-of-the-art baselines while maintaining valid coverage.