{"paper":{"title":"Minkowski-Type Wasserstein Metrics and Barycenters for Location-Scale Mixtures with Application to Domain Adaptation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Songyan Luo, Yunxin Zhang","submitted_at":"2026-06-25T00:42:28Z","abstract_excerpt":"Discrete optimal transport (OT) typically relies on pointwise matching between empirical measures, incurring computational costs that scale at least quadratically with the sample size. To circumvent this limitation, we introduce a mathematical framework for OT between finite location-scale mixture models. By defining a specific function class grounded in generalized Minkowski inequalities and characterizing OT maps between multivariate location-scale families, we extend Wasserstein-type metrics and barycenters to these mixture models under the assumption of identifiability. Furthermore, we pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26482","kind":"arxiv","version":1},"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/2606.26482/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"}