{"paper":{"title":"Compressed Regression","license":"","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"stat.ML","authors_text":"John Lafferty, Larry Wasserman, Shuheng Zhou","submitted_at":"2007-06-04T20:42:54Z","abstract_excerpt":"Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that $\\ell_1$-regularized least squares regression can accurately estimate a sparse linear model from $n$ noisy examples in $p$ dimensions, even if $p$ is much larger than $n$. In this paper we study a variant of this problem where the original $n$ input variables are compressed by a random linear transformation to $m \\ll n$ examples in $p$ dimensions, and establish conditions under whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0534","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"}