Aggregating Conformal Prediction Sets via α-Allocation

• URL: http://arxiv.org/abs/2511.12065v1
• Date: Sat, 15 Nov 2025 07:11:21 GMT
• Title: Aggregating Conformal Prediction Sets via α-Allocation
• Authors: Congbin Xu, Yue Yu, Haojie Ren, Zhaojun Wang, Changliang Zou,
• Abstract summary: This work introduces a principled aggregation strategy that optimally allocates confidence levels across multiple conformal prediction sets.<n>Experiments on synthetic and real-world datasets demonstrate that COLA achieves considerably smaller prediction sets than state-of-the-art baselines.
• Score: 22.63151097928744
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Conformal prediction offers a distribution-free framework for constructing prediction sets with finite-sample coverage. Yet, efficiently leveraging multiple conformity scores to reduce prediction set size remains a major open challenge. Instead of selecting a single best score, this work introduces a principled aggregation strategy, COnfidence-Level Allocation (COLA), that optimally allocates confidence levels across multiple conformal prediction sets to minimize empirical set size while maintaining provable coverage. Two variants are further developed, COLA-s and COLA-f, which guarantee finite-sample marginal coverage via sample splitting and full conformalization, respectively. In addition, we develop COLA-l, an individualized allocation strategy that promotes local size efficiency while achieving asymptotic conditional coverage. Extensive experiments on synthetic and real-world datasets demonstrate that COLA achieves considerably smaller prediction sets than state-of-the-art baselines while maintaining valid coverage.

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