{"paper":{"title":"Low Rank Estimation of Similarities on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Pedro Rangel, Vladimir Koltchinskii","submitted_at":"2012-05-09T04:22:23Z","abstract_excerpt":"Let (V, E) be a graph with vertex set V and edge set E. Let (X, X', Y) \\in V \\times V \\times {-1, 1} be a random triple, where X, X' are independent uniformly distributed vertices and Y is a label indicating whether X, X' are \"similar\" (Y = +1), or not (Y = -1). Our goal is to estimate the regression function S\\ast (u, v) = E(Y |X = u, X = v), u, v \\in V based on training data consisting of n i.i.d. copies of (X, X',Y). We are interested in this problem in the case when S\\ast is a symmetric low rank kernel and, in addition to this, it is assumed that S\\ast is \"smooth\" on the graph. We study es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1868","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":""},"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"}