{"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/sampling-sketches-for-concave-sublinear-1","title":"Sampling Sketches for Concave Sublinear Functions of Frequencies","arxiv_id":"1907.02218","date":"2019-07-04","proceeding":null,"authors":["Edith Cohen","Ofir Geri"],"abstract":"We consider massive distributed datasets that consist of elements modeled as key-value pairs and the task of computing statistics or aggregates where the contribution of each key is weighted by a function of its frequency (sum of values of its elements). This fundamental problem has a wealth of applications in data analytics and machine learning, in particular, with concave sublinear functions of the frequencies that mitigate the disproportionate effect of keys with high frequency. The family of concave sublinear functions includes low frequency moments ($p \\leq 1$), capping, logarithms, and their compositions. A common approach is to sample keys, ideally, proportionally to their contributions and estimate statistics from the sample. A simple but costly way to do this is by aggregating the data to produce a table of keys and their frequencies, apply our function to the frequency values, and then apply a weighted sampling scheme. Our main contribution is the design of composable sampling sketches that can be tailored to any concave sublinear function of the frequencies. Our sketch structure size is very close to the desired sample size and our samples provide statistical guarantees on the estimation quality that are very close to that of an ideal sample of the same size computed over aggregated data. Finally, we demonstrate experimentally the simplicity and effectiveness of our methods.","url_abs":"http://arxiv.org/abs/1907.02218v3","url_pdf":"http://arxiv.org/pdf/1907.02218v3.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":"sampling-sketches-for-concave-sublinear-1","repo_url":"https://github.com/ofirgeri/concave-sublinear-sampling","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1907.02218","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1907.02218"}},"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/ofirgeri/concave-sublinear-sampling","reach":null}],"summary":{"ran_honours":1,"unverified":2},"by_repo_kind":{"official":{"samples":3,"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":3,"samples":[{"code_sha256_prefix":"99c5500378375a7c","entry":"seedCDF","repo":"ofirgeri/concave-sublinear-sampling","repo_kind":"official","path":"sketch.py","file_url":"https://github.com/ofirgeri/concave-sublinear-sampling/blob/HEAD/sketch.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"99c5500378375a7c"}},{"code_sha256_prefix":"7a57eb01ee0219a0","entry":"exp_hashed","repo":"ofirgeri/concave-sublinear-sampling","repo_kind":"official","path":"sketch.py","file_url":"https://github.com/ofirgeri/concave-sublinear-sampling/blob/HEAD/sketch.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":"7a57eb01ee0219a0"}},{"code_sha256_prefix":"fabc15e49b314588","entry":"hashed_float","repo":"ofirgeri/concave-sublinear-sampling","repo_kind":"official","path":"sketch.py","file_url":"https://github.com/ofirgeri/concave-sublinear-sampling/blob/HEAD/sketch.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":"fabc15e49b314588"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}