{"paper":{"title":"The Optimal Hard Threshold for Singular Values is 4/sqrt(3)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"David L. Donoho, Matan Gavish","submitted_at":"2013-05-24T23:54:18Z","abstract_excerpt":"We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, where singular values below a prescribed threshold $\\lambda$ are set to 0. We study the asymptotic MSE in a framework where the matrix size is large compared to the rank of the matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. The AMSE-optimal choice of hard threshold, in the case of n-by-n matrix in noise level \\sigma, is simply $(4/\\sqrt{3}) \\sqrt{n}\\sigma \\approx 2.309 \\sqrt{n}\\sigma$ when $\\sigma$ is known, or simply $2.858\\cdot y_{med}$ when $\\sigma$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5870","kind":"arxiv","version":3},"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"}