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We consider here the case where such prediction sets come after a selection process. The selection process requires that the selected prediction sets be \u2018informative\u2019 in a well-defined sense. We consider both the classification and regression settings where the analyst may consider as informative only the sample with prediction sets small enough, excluding null values, or obeying other appropriate \u2018monotone\u2019 constraints. We develop a unified framework for building such informative conformal prediction sets while controlling the false coverage rate (FCR) on the selected sample. While conformal prediction sets after selection have been the focus of much recent literature in the field, the new introduced procedures, called InfoSP and InfoSCOP, are to our knowledge the first ones providing FCR control for informative prediction sets. We show the usefulness of our resulting procedures on real and simulated data.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkae120","type":"journal-article","created":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T07:16:30Z","timestamp":1736147790000},"page":"909-929","source":"Crossref","is-referenced-by-count":3,"title":["Selecting informative conformal prediction sets with false coverage rate control"],"prefix":"10.1093","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1442-537X","authenticated-orcid":false,"given":"Ulysse","family":"Gazin","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris Cit\u00e9 and Sorbonne Universit\u00e9, CNRS, Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation, F-75013 Paris ,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruth","family":"Heller","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, Tel-Aviv University , Tel-Aviv 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