{"paper":{"title":"Approximate Sparse Linear Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Piotr Indyk, Sariel Har-Peled, Sepideh Mahabadi","submitted_at":"2016-09-28T02:36:46Z","abstract_excerpt":"In the Sparse Linear Regression (SLR) problem, given a $d \\times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\\tau$ such that the error $||M \\tau-q||$ is minimized. This problem is equivalent to the following geometric problem: given a set $P$ of $n$ points and a query point $q$ in $d$ dimensions, find the closest $k$-dimensional subspace to $q$, that is spanned by a subset of $k$ points in $P$. In this paper, we present data-structures/algorithms and conditional lower bounds for several variants of this problem (such as finding the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08739","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"}