{"paper":{"title":"Low rank estimation of smooth kernels 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":"2012-07-19T21:56:18Z","abstract_excerpt":"Let (V,A) be a weighted graph with a finite vertex set V, with a symmetric matrix of nonnegative weights A and with Laplacian $\\Delta$. Let $S_*:V\\times V\\mapsto{\\mathbb{R}}$ be a symmetric kernel defined on the vertex set V. Consider n i.i.d. observations $(X_j,X_j',Y_j),j=1,\\ldots,n$, where $X_j,X_j'$ are independent random vertices sampled from the uniform distribution in V and $Y_j\\in{\\mathbb{R}}$ is a real valued response variable such that ${\\mathbb{E}}(Y_j|X_j,X_j')=S_*(X_j,X_j'),j=1,\\ldots,n$. The goal is to estimate the kernel $S_*$ based on the data $(X_1,X_1',Y_1),\\ldots,(X_n,X_n',Y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4819","kind":"arxiv","version":4},"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"}