{"paper":{"title":"Topics in Matrix Sampling Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christos Boutsidis","submitted_at":"2011-05-04T00:19:49Z","abstract_excerpt":"We study three fundamental problems of Linear Algebra, lying in the heart of various Machine Learning applications, namely: 1)\"Low-rank Column-based Matrix Approximation\". We are given a matrix A and a target rank k. The goal is to select a subset of columns of A and, by using only these columns, compute a rank k approximation to A that is as good as the rank k approximation that would have been obtained by using all the columns; 2) \"Coreset Construction in Least-Squares Regression\". We are given a matrix A and a vector b. Consider the (over-constrained) least-squares problem of minimizing ||A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0709","kind":"arxiv","version":1},"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"}