{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/screenot-exact-mse-optimal-singular-value","title":"ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise","arxiv_id":"2009.12297","date":"2020-09-25","proceeding":null,"authors":["David L. Donoho","Matan Gavish","Elad Romanov"],"abstract":"We derive a formula for optimal hard thresholding of the singular value decomposition in the presence of correlated additive noise; although it nominally involves unobservables, we show how to apply it even where the noise covariance structure is not a-priori known or is not independently estimable. The proposed method, which we call ScreeNOT, is a mathematically solid alternative to Cattell's ever-popular but vague Scree Plot heuristic from 1966. ScreeNOT has a surprising oracle property: it typically achieves exactly, in large finite samples, the lowest possible MSE for matrix recovery, on each given problem instance - i.e. the specific threshold it selects gives exactly the smallest achievable MSE loss among all possible threshold choices for that noisy dataset and that unknown underlying true low rank model. The method is computationally efficient and robust against perturbations of the underlying covariance structure. Our results depend on the assumption that the singular values of the noise have a limiting empirical distribution of compact support; this model, which is standard in random matrix theory, is satisfied by many models exhibiting either cross-row correlation structure or cross-column correlation structure, and also by many situations where there is inter-element correlation structure. Simulations demonstrate the effectiveness of the method even at moderate matrix sizes. The paper is supplemented by ready-to-use software packages implementing the proposed algorithm: package ScreeNOT in Python (via PyPI) and R (via CRAN).","url_abs":"https://arxiv.org/abs/2009.12297v3","url_pdf":"https://arxiv.org/pdf/2009.12297v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"screenot-exact-mse-optimal-singular-value","repo_url":"https://github.com/eladromanov/screenot","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2009.12297","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2009.12297"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/eladromanov/screenot","reach":null}],"summary":{"ran_fixture":3},"by_repo_kind":{"official":{"samples":3,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"618ed03eadbc68b0","entry":"adaptiveHardThresholding","repo":"eladromanov/screenot","repo_kind":"official","path":"Python/src/screenot/ScreeNOT.py","file_url":"https://github.com/eladromanov/screenot/blob/HEAD/Python/src/screenot/ScreeNOT.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"618ed03eadbc68b0"}},{"code_sha256_prefix":"c034829259fe2355","entry":"computeOptThreshold","repo":"eladromanov/screenot","repo_kind":"official","path":"Python/src/screenot/ScreeNOT.py","file_url":"https://github.com/eladromanov/screenot/blob/HEAD/Python/src/screenot/ScreeNOT.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c034829259fe2355"}},{"code_sha256_prefix":"f6c2e9e5e5a6007b","entry":"createPseudoNoise","repo":"eladromanov/screenot","repo_kind":"official","path":"Python/src/screenot/ScreeNOT.py","file_url":"https://github.com/eladromanov/screenot/blob/HEAD/Python/src/screenot/ScreeNOT.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f6c2e9e5e5a6007b"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}