{"paper":{"title":"Integral Probability Metrics on submanifolds: interpolation inequalities and optimal inference","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Arthur St\\'ephanovitch","submitted_at":"2024-06-03T12:30:23Z","abstract_excerpt":"We study interpolation inequalities between H\\\"older Integral Probability Metrics (IPMs) in the case where the measures have densities on closed submanifolds. Precisely, it is shown that if two probability measures $\\mu$ and $\\mu^\\star$ have $\\beta$-smooth densities with respect to the volume measure of some submanifolds $\\mathcal{M}$ and $\\mathcal{M}^\\star$ respectively, then the H\\\"older IPMs $d_{\\mathcal{H}^\\gamma_1}$ of smoothness $\\gamma\\geq 1$ and $d_{\\mathcal{H}^\\eta_1}$ of smoothness $\\eta>\\gamma$, satisfy $d_{ \\mathcal{H}_1^{\\gamma}}(\\mu,\\mu^\\star)\\lesssim d_{ \\mathcal{H}_1^{\\eta}}(\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01268","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.01268/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}