{"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/sketchy-decisions-convex-low-rank-matrix","title":"Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage","arxiv_id":"1702.06838","date":"2017-02-22","proceeding":null,"authors":["Alp Yurtsever","Madeleine Udell","Joel A. Tropp","Volkan Cevher"],"abstract":"This paper concerns a fundamental class of convex matrix optimization\nproblems. It presents the first algorithm that uses optimal storage and\nprovably computes a low-rank approximation of a solution. In particular, when\nall solutions have low rank, the algorithm converges to a solution. This\nalgorithm, SketchyCGM, modifies a standard convex optimization scheme, the\nconditional gradient method, to store only a small randomized sketch of the\nmatrix variable. After the optimization terminates, the algorithm extracts a\nlow-rank approximation of the solution from the sketch. In contrast to\nnonconvex heuristics, the guarantees for SketchyCGM do not rely on statistical\nmodels for the problem data. Numerical work demonstrates the benefits of\nSketchyCGM over heuristics.","url_abs":"http://arxiv.org/abs/1702.06838v1","url_pdf":"http://arxiv.org/pdf/1702.06838v1.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":"abstracts"},"code_links":[{"paper_slug":"sketchy-decisions-convex-low-rank-matrix","repo_url":"https://github.com/dseuss/pyscgm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1702.06838","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1702.06838"}},"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/dseuss/pyscgm","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"summary":{"unverified":3},"by_repo_kind":{"listed":{"samples":3,"ran":0,"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":"c28f1e1c1661d7fe","entry":"approx_range_finder","repo":"dseuss/pyscgm","repo_kind":"listed","path":"pyscgm/linalg.py","file_url":"https://github.com/dseuss/pyscgm/blob/HEAD/pyscgm/linalg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"c28f1e1c1661d7fe"}},{"code_sha256_prefix":"90f24189441eb0b4","entry":"eigsh","repo":"dseuss/pyscgm","repo_kind":"listed","path":"pyscgm/linalg.py","file_url":"https://github.com/dseuss/pyscgm/blob/HEAD/pyscgm/linalg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"90f24189441eb0b4"}},{"code_sha256_prefix":"2915802528cdd374","entry":"svds","repo":"dseuss/pyscgm","repo_kind":"listed","path":"pyscgm/linalg.py","file_url":"https://github.com/dseuss/pyscgm/blob/HEAD/pyscgm/linalg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"2915802528cdd374"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}