{"paper":{"title":"Leveraged volume sampling for linear regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Daniel Hsu, Manfred K. Warmuth, Micha{\\l} Derezi\\'nski","submitted_at":"2018-02-19T18:35:39Z","abstract_excerpt":"Suppose an $n \\times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \\ll n$ of the responses, and then produce a weight vector whose sum of squares loss over all points is at most $1+\\epsilon$ times the minimum. When $k$ is very small (e.g., $k=d$), jointly sampling diverse subsets of points is crucial. One such method called volume sampling has a unique and desirable property that the weight vector it produces is an unbiased estimate of the optimum. It is therefore nat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06749","kind":"arxiv","version":3},"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"}