{"paper":{"title":"The Vertex Sample Complexity of Free Energy is Polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.LG","authors_text":"Elchanan Mossel, Frederic Koehler, Vishesh Jain","submitted_at":"2018-02-16T21:25:42Z","abstract_excerpt":"We study the following question: given a massive Markov random field on $n$ nodes, can a small sample from it provide a rough approximation to the free energy $\\mathcal{F}_n = \\log{Z_n}$?\n  Results in graph limit literature by Borgs, Chayes, Lov\\'asz, S\\'os, and Vesztergombi show that for Ising models on $n$ nodes and interactions of strength $\\Theta(1/n)$, an $\\epsilon$ approximation to $\\log Z_n / n$ can be achieved by sampling a randomly induced model on $2^{O(1/\\epsilon^2)}$ nodes. We show that the sampling complexity of this problem is {\\em polynomial in} $1/\\epsilon$. We further show a p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06129","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"}