{"paper":{"title":"Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Boaz Barak, David Steurer, Jonathan A. Kelner","submitted_at":"2014-07-06T20:42:05Z","abstract_excerpt":"We give a new approach to the dictionary learning (also known as \"sparse coding\") problem of recovering an unknown $n\\times m$ matrix $A$ (for $m \\geq n$) from examples of the form \\[ y = Ax + e, \\] where $x$ is a random vector in $\\mathbb R^m$ with at most $\\tau m$ nonzero coordinates, and $e$ is a random noise vector in $\\mathbb R^n$ with bounded magnitude. For the case $m=O(n)$, our algorithm recovers every column of $A$ within arbitrarily good constant accuracy in time $m^{O(\\log m/\\log(\\tau^{-1}))}$, in particular achieving polynomial time if $\\tau = m^{-\\delta}$ for any $\\delta>0$, and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1543","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"}