Aggregating conformal prediction sets via $ \alpha $-allocation

• 成果类型: Article
• 署名作者: Xu, Congbin; Yu, Yue; Wang, Zhaojun; Zou, Changliang; Ren, Haojie
• 署名单位: Nankai University; Nankai University; Shanghai Jiao Tong University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asag048
• 发表日期: 2026
• 页码: asag048
• 关键词: Conditional coverage; conformal inference; Individualized decision; model averaging; optimization

摘要

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, with confidence levels allocated optimally to minimize the 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.