{"paper":{"title":"Vector Quantile Regression: An Optimal Transport Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Alfred Galichon, Guillaume Carlier, Victor Chernozhukov","submitted_at":"2014-06-18T08:59:52Z","abstract_excerpt":"We propose a notion of conditional vector quantile function and a vector quantile regression. A \\emph{conditional vector quantile function} (CVQF) of a random vector $Y$, taking values in $\\mathbb{R}^d$ given covariates $Z=z$, taking values in $\\mathbb{R}% ^k$, is a map $u \\longmapsto Q_{Y\\mid Z}(u,z)$, which is monotone, in the sense of being a gradient of a convex function, and such that given that vector $U$ follows a reference non-atomic distribution $F_U$, for instance uniform distribution on a unit cube in $\\mathbb{R}^d$, the random vector $Q_{Y\\mid Z}(U,z)$ has the distribution of $Y$ c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4643","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}