{"paper":{"title":"Approximation algorithms for the normalizing constant of Gibbs distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.PR","authors_text":"Mark Huber","submitted_at":"2012-06-12T23:49:36Z","abstract_excerpt":"Consider a family of distributions $\\{\\pi_{\\beta}\\}$ where $X\\sim\\pi_{\\beta}$ means that $\\mathbb{P}(X=x)=\\exp(-\\beta H(x))/Z(\\beta)$. Here $Z(\\beta)$ is the proper normalizing constant, equal to $\\sum_x\\exp(-\\beta H(x))$. Then $\\{\\pi_{\\beta}\\}$ is known as a Gibbs distribution, and $Z(\\beta)$ is the partition function. This work presents a new method for approximating the partition function to a specified level of relative accuracy using only a number of samples, that is, $O(\\ln(Z(\\beta))\\ln(\\ln(Z(\\beta))))$ when $Z(0)\\geq1$. This is a sharp improvement over previous, similar approaches that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2689","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"}