{"paper":{"title":"Testing to distinguish measures on metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","stat.ML"],"primary_cat":"stat.ME","authors_text":"Andrew J. Blumberg, Prithwish Bhaumik, Stephen G. Walker","submitted_at":"2018-02-04T16:25:53Z","abstract_excerpt":"We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces $({\\mathbb X}, d, \\mu_1)$ and $({\\mathbb X}, d, \\mu_2)$, we are interested in the problem of determining from finite data whether or not $\\mu_1$ is $\\mu_2$. The key is to use pairwise distances between observations and, employing a reconstruction theorem of Gromov, we can perform such a test using a two sample Kolmogorov--Smirnov test. A real analysis using phylogenetic trees and flu data is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01152","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":""},"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"}