{"paper":{"title":"An improved analysis of the ER-SpUD dictionary learning algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","math.IT","math.PR"],"primary_cat":"cs.LG","authors_text":"Jaros{\\l}aw B{\\l}asiok, Jelani Nelson","submitted_at":"2016-02-18T08:51:08Z","abstract_excerpt":"In \"dictionary learning\" we observe $Y = AX + E$ for some $Y\\in\\mathbb{R}^{n\\times p}$, $A \\in\\mathbb{R}^{m\\times n}$, and $X\\in\\mathbb{R}^{m\\times p}$. The matrix $Y$ is observed, and $A, X, E$ are unknown. Here $E$ is \"noise\" of small norm, and $X$ is column-wise sparse. The matrix $A$ is referred to as a {\\em dictionary}, and its columns as {\\em atoms}. Then, given some small number $p$ of samples, i.e.\\ columns of $Y$, the goal is to learn the dictionary $A$ up to small error, as well as $X$. The motivation is that in many applications data is expected to sparse when represented by atoms i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05719","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"}