{"id":8509,"date":"2025-11-20T07:02:27","date_gmt":"2025-11-20T07:02:27","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/11\/20\/2511-15146\/"},"modified":"2025-11-20T07:02:27","modified_gmt":"2025-11-20T07:02:27","slug":"2511-15146","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/11\/20\/2511-15146\/","title":{"rendered":"Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distribution to Multivariate Settings"},"content":{"rendered":"

Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distribution to Multivariate Settings
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arXiv:2511.15146v1 Announce Type: new
\nAbstract: 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.<\/div>\n

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\n Eugene Ndiaye
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Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distribution to Multivariate Settings arXiv:2511.15146v1 Announce Type: new Abstract: 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 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,190,112,191],"tags":[582,1673,384],"class_list":["post-8509","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-st","category-stat-ml","category-stat-th","tag-distribution","tag-multivariate","tag-uncertainty"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8509"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=8509"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8509\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=8509"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=8509"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=8509"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}