{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T00:18:37Z","timestamp":1789172317031,"version":"build-2803163510"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,6]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>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.<\/jats:p>","DOI":"10.1093\/biomet\/asag048","type":"journal-article","created":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T11:35:20Z","timestamp":1784633720000},"source":"Crossref","is-referenced-by-count":0,"title":["Aggregating conformal prediction sets via $ \\alpha $-allocation"],"prefix":"10.1093","volume":"113","author":[{"given":"Congbin","family":"Xu","sequence":"first","affiliation":[{"name":"School of Statistics and Data Science, Nankai University , 94 Weijin Road , Tianjin 300071, \u00a0 congbinxu@mail.nankai.edu.cn","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Nankai University , 94 Weijin Road , Tianjin 300071, \u00a0 yyu@mail.nankai.edu.cn","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhaojun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Nankai University , 94 Weijin Road , Tianjin 300071, \u00a0 zjwangnk@126.com","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changliang","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Nankai University , 94 Weijin Road , Tianjin 300071,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haojie","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University , 800 Dongchuan Road , Shanghai 200240,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,7,21]]},"reference":[{"key":"2026091119565650800_asag048-B1","first-page":"455","article-title":"The limits of distribution-free conditional predictive inference","volume":"10","author":"Barber","year":"2021","journal-title":"Info. 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