{"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/fast-exact-leverage-score-sampling-from-1","title":"Fast Exact Leverage Score Sampling from Khatri-Rao Products with Applications to Tensor Decomposition","arxiv_id":"2301.12584","date":"2023-01-29","proceeding":null,"authors":["Vivek Bharadwaj","Osman Asif Malik","Riley Murray","Laura Grigori","Aydin Buluc","James Demmel"],"abstract":"We present a data structure to randomly sample rows from the Khatri-Rao product of several matrices according to the exact distribution of its leverage scores. Our proposed sampler draws each row in time logarithmic in the height of the Khatri-Rao product and quadratic in its column count, with persistent space overhead at most the size of the input matrices. As a result, it tractably draws samples even when the matrices forming the Khatri-Rao product have tens of millions of rows each. When used to sketch the linear least squares problems arising in CANDECOMP / PARAFAC tensor decomposition, our method achieves lower asymptotic complexity per solve than recent state-of-the-art methods. Experiments on billion-scale sparse tensors validate our claims, with our algorithm achieving higher accuracy than competing methods as the decomposition rank grows.","url_abs":"https://arxiv.org/abs/2301.12584v4","url_pdf":"https://arxiv.org/pdf/2301.12584v4.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":"fast-exact-leverage-score-sampling-from-1","repo_url":"https://github.com/vbharadwaj-bk/fast_tensor_leverage","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2301.12584","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2301.12584"}},"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/vbharadwaj-bk/fast_tensor_leverage","reach":null}],"summary":{"ran_violates":1,"unverified":1},"by_repo_kind":{"official":{"samples":2,"ran":1,"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":2,"samples":[{"code_sha256_prefix":"f73cb2732592610b","entry":"chain_had_prod","repo":"vbharadwaj-bk/fast_tensor_leverage","repo_kind":"official","path":"reference_implementation/krp_sampler.py","file_url":"https://github.com/vbharadwaj-bk/fast_tensor_leverage/blob/HEAD/reference_implementation/krp_sampler.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f73cb2732592610b"}},{"code_sha256_prefix":"413e66416640cfcb","entry":"ReferenceKRPSampler","repo":"vbharadwaj-bk/fast_tensor_leverage","repo_kind":"official","path":"reference_implementation/krp_sampler.py","file_url":"https://github.com/vbharadwaj-bk/fast_tensor_leverage/blob/HEAD/reference_implementation/krp_sampler.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"413e66416640cfcb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}