{"paper":{"title":"Approximate Guarantees for Dictionary Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Aditya Bhaskara, Wai Ming Tai","submitted_at":"2019-05-28T21:11:27Z","abstract_excerpt":"In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\\mathbb{R}^d$), and the goal is to find a \"basis\" in which the signals have a sparse (approximate) representation. The problem has received a lot of attention in signal processing, learning, and theoretical computer science. The problem is formalized as factorizing a matrix $X (d \\times n)$ (whose columns are the signals) as $X = AY$, where $A$ has a prescribed number $m$ of columns (typically $m \\ll n$), and $Y$ has columns that are $k$-sparse (typically $k \\ll d$). Most of the known theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12091","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"}