{"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/small-coresets-via-negative-dependence-dpps","title":"Small coresets via negative dependence: DPPs, linear statistics, and concentration","arxiv_id":"2411.00611","date":"2024-11-01","proceeding":null,"authors":["Rémi Bardenet","Subhroshekhar Ghosh","Hugo Simon-Onfroy","Hoang-Son Tran"],"abstract":"Determinantal point processes (DPPs) are random configurations of points with tunable negative dependence. Because sampling is tractable, DPPs are natural candidates for subsampling tasks, such as minibatch selection or coreset construction. A \\emph{coreset} is a subset of a (large) training set, such that minimizing an empirical loss averaged over the coreset is a controlled replacement for the intractable minimization of the original empirical loss. Typically, the control takes the form of a guarantee that the average loss over the coreset approximates the total loss uniformly across the parameter space. Recent work has provided significant empirical support in favor of using DPPs to build randomized coresets, coupled with interesting theoretical results that are suggestive but leave some key questions unanswered. In particular, the central question of whether the cardinality of a DPP-based coreset is fundamentally smaller than one based on independent sampling remained open. In this paper, we answer this question in the affirmative, demonstrating that \\emph{DPPs can provably outperform independently drawn coresets}. In this vein, we contribute a conceptual understanding of coreset loss as a \\emph{linear statistic} of the (random) coreset. We leverage this structural observation to connect the coresets problem to a more general problem of concentration phenomena for linear statistics of DPPs, wherein we obtain \\emph{effective concentration inequalities that extend well-beyond the state-of-the-art}, encompassing general non-projection, even non-symmetric kernels. The latter have been recently shown to be of interest in machine learning beyond coresets, but come with a limited theoretical toolbox, to the extension of which our result contributes. Finally, we are also able to address the coresets problem for vector-valued objective functions, a novelty in the coresets literature.","url_abs":"https://arxiv.org/abs/2411.00611v1","url_pdf":"https://arxiv.org/pdf/2411.00611v1.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":"small-coresets-via-negative-dependence-dpps","repo_url":"https://github.com/hsimonfroy/dppcoresets","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"point-processes","task_name":"Point Processes"}],"methods":[{"method_slug":"coresets","method_name":"Coresets"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2411.00611","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2411.00611"}},"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":"deterministic:regex_extraction","url":"https://github.com/hsimonfroy/DPPcoresets","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/hsimonfroy/dppcoresets","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_honours":1,"unverified":3},"by_repo_kind":{"official":{"samples":4,"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":0,"samples":[{"code_sha256_prefix":"5427726757f681b9","entry":"compute_ordering","repo":"hsimonfroy/DPPcoresets","repo_kind":"official","path":"src/samplers.py","file_url":"https://github.com/hsimonfroy/DPPcoresets/blob/HEAD/src/samplers.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5427726757f681b9"}},{"code_sha256_prefix":"d7141222ec835704","entry":"get_disk_data","repo":"hsimonfroy/dppcoresets","repo_kind":"official","path":"src/utils.py","file_url":"https://github.com/hsimonfroy/dppcoresets/blob/HEAD/src/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d7141222ec835704"}},{"code_sha256_prefix":"e6150a8648e8b4a2","entry":"get_evenly_spaced_circle","repo":"hsimonfroy/dppcoresets","repo_kind":"official","path":"src/utils.py","file_url":"https://github.com/hsimonfroy/dppcoresets/blob/HEAD/src/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e6150a8648e8b4a2"}},{"code_sha256_prefix":"01f5c3019993be7a","entry":"get_hypercube_data","repo":"hsimonfroy/dppcoresets","repo_kind":"official","path":"src/utils.py","file_url":"https://github.com/hsimonfroy/dppcoresets/blob/HEAD/src/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"01f5c3019993be7a"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}