{"paper":{"title":"Concentration Inequalities for Incomplete U-statistics over Arbitrary Sampling Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Zheng Tracy Ke","submitted_at":"2026-07-19T03:25:32Z","abstract_excerpt":"Let $X_1, X_2, \\ldots, X_n$ be independent random vectors. For a directed graph $G=(V,E)$ with vertex set $V=\\{1,2,\\ldots,n\\}$ and a collection of bivariate kernels $\\{h_e:e\\in E\\}$, we consider \\[ U=\\sum_{e=(i,j)\\in E} h_e(X_i,X_j). \\] This framework generalizes incomplete U-statistics by allowing the random vectors to be non-identically distributed, the kernels to be asymmetric and edge-dependent, and the sampling structure to be specified by an arbitrary graph.\n  We derive several concentration inequalities for $U-\\mathbb{E}U$. The main proof strategy exploits edge-coloring results from gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17048","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/2607.17048/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"}