{"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/kernel-quadrature-with-dpps","title":"Kernel quadrature with DPPs","arxiv_id":"1906.07832","date":"2019-06-18","proceeding":"NeurIPS 2019 12","authors":["Ayoub Belhadji","Rémi Bardenet","Pierre Chainais"],"abstract":"We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the quadrature error, that depends on the spectrum of the RKHS kernel. Finally, we experimentally compare DPPs to existing kernel-based quadratures such as herding, Bayesian quadrature, or leverage score sampling. Numerical results confirm the interest of DPPs, and even suggest faster rates than our bounds in particular cases.","url_abs":"https://arxiv.org/abs/1906.07832v3","url_pdf":"https://arxiv.org/pdf/1906.07832v3.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":"kernel-quadrature-with-dpps","repo_url":"https://github.com/AyoubBelhadji/DPPKQ","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1906.07832","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1906.07832"}},"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/AyoubBelhadji/DPPKQ","reach":null}],"summary":{"ran_draft_wrong":2,"ran_fixture":1},"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":"02469948b77a3550","entry":"Gaussian_kernel","repo":"AyoubBelhadji/DPPKQ","repo_kind":"official","path":"kernels/Gaussian_kernel.py","file_url":"https://github.com/AyoubBelhadji/DPPKQ/blob/HEAD/kernels/Gaussian_kernel.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"02469948b77a3550"}},{"code_sha256_prefix":"f800d1a4f2693b41","entry":"get_kernel_matrix_Gaussian_kernel","repo":"AyoubBelhadji/DPPKQ","repo_kind":"official","path":"kernels/Gaussian_kernel.py","file_url":"https://github.com/AyoubBelhadji/DPPKQ/blob/HEAD/kernels/Gaussian_kernel.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":"f800d1a4f2693b41"}},{"code_sha256_prefix":"542ae81107a57fb7","entry":"mean_element","repo":"AyoubBelhadji/DPPKQ","repo_kind":"official","path":"kernels/Gaussian_kernel.py","file_url":"https://github.com/AyoubBelhadji/DPPKQ/blob/HEAD/kernels/Gaussian_kernel.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"542ae81107a57fb7"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}