{"paper":{"title":"Nearly-optimal bounds for sparse recovery in generic norms, with applications to $k$-median sketching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Arturs Backurs, David P. Woodruff, Eric Price, Ilya Razenshteyn, Piotr Indyk","submitted_at":"2015-04-05T02:59:25Z","abstract_excerpt":"We initiate the study of trade-offs between sparsity and the number of measurements in sparse recovery schemes for generic norms. Specifically, for a norm $\\|\\cdot\\|$, sparsity parameter $k$, approximation factor $K>0$, and probability of failure $P>0$, we ask: what is the minimal value of $m$ so that there is a distribution over $m \\times n$ matrices $A$ with the property that for any $x$, given $Ax$, we can recover a $k$-sparse approximation to $x$ in the given norm with probability at least $1-P$? We give a partial answer to this problem, by showing that for norms that admit efficient linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01076","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"}