{"paper":{"title":"An optimal $(\\epsilon,\\delta)$-approximation scheme for the mean of random variables with bounded relative variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"Mark Huber","submitted_at":"2017-06-05T18:09:36Z","abstract_excerpt":"Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\\{0,1\\}$-matrix, and many others) reduce to creating random variables $X_1,X_2,\\ldots$ with finite mean $\\mu$ and standard deviation$\\sigma$ such that $\\mu$ is the solution for the problem input, and the relative standard deviation $|\\sigma/\\mu| \\leq c$ for known $c$. Under these circumstances, it is known that the number of samples from the $\\{X_i\\}$ needed to form an $(\\epsilon,\\delta)$-approximation $\\hat \\mu$ that satisf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01478","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"}