BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Département de mathématiques et applications
X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20260329T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20261025T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260423T110000
DTEND;TZID=Europe/Paris:20260423T120000
DTSTAMP:20260423T065326
CREATED:20260420T090126Z
LAST-MODIFIED:20260420T090126Z
UID:21319-1776942000-1776945600@www.math.ens.psl.eu
SUMMARY:Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distribution to Multivariate Settings
DESCRIPTION:Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the scores observed on a set of calibration examples. However\, this procedure is only straightforward when scores are scalar-valued\, which has limited CP to real-valued scores or ad-hoc reductions to one dimension. The problem of ordering vectors has been studied via optimal transport (OT)\, which provides a principled method for defining vector-ranks and multivariate quantile regions\, though typically with only asymptotic coverage guarantees. We restore finite-sample\, distribution-free coverage by conformalizing the vector-valued OT quantile region. Here\, a candidate’s rank is defined via a transport map computed for the calibration scores augmented with that candidate’s score. This defines a continuum of OT problems for which we prove that the resulting optimal assignment is piecewise-constant across a fixed polyhedral partition of the score space. This allows us to characterize the entire prediction set tractably\, and provides the machinery to address a deeper limitation of prediction sets: that they only indicate which outcomes are plausible\, but not their relative likelihood. In one dimension\, conformal predictive distributions (CPDs) fill this gap by producing a predictive distribution with finite-sample calibration. Extending CPDs beyond one dimension remained an open problem. We construct\, to our knowledge\, the first multivariate CPDs with finite-sample calibration\, i.e.\, they define a valid multivariate distribution where any derived uncertainty region automatically has guaranteed coverage. We present both conservative and exact randomized versions\, the latter resulting in a multivariate generalization of the classical Dempster-Hill procedure.
URL:https://www.math.ens.psl.eu/evenement/beyond-uncertainty-sets-leveraging-optimal-transport-to-extend-conformal-predictive-distribution-to-multivariate-settings/
LOCATION:Salle W
CATEGORIES:CSD seminar
END:VEVENT
END:VCALENDAR