{"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/kronecker-determinantal-point-processes","title":"Kronecker Determinantal Point Processes","arxiv_id":"1605.08374","date":"2016-05-26","proceeding":"NeurIPS 2016 12","authors":["Zelda Mariet","Suvrit Sra"],"abstract":"Determinantal Point Processes (DPPs) are probabilistic models over all\nsubsets a ground set of $N$ items. They have recently gained prominence in\nseveral applications that rely on \"diverse\" subsets. However, their\napplicability to large problems is still limited due to the $\\mathcal O(N^3)$\ncomplexity of core tasks such as sampling and learning. We enable efficient\nsampling and learning for DPPs by introducing KronDPP, a DPP model whose kernel\nmatrix decomposes as a tensor product of multiple smaller kernel matrices. This\ndecomposition immediately enables fast exact sampling. But contrary to what one\nmay expect, leveraging the Kronecker product structure for speeding up DPP\nlearning turns out to be more difficult. We overcome this challenge, and derive\nbatch and stochastic optimization algorithms for efficiently learning the\nparameters of a KronDPP.","url_abs":"http://arxiv.org/abs/1605.08374v1","url_pdf":"http://arxiv.org/pdf/1605.08374v1.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":"kronecker-determinantal-point-processes","repo_url":"https://github.com/UnofficialJuliaMirror/DeterminantalPointProcesses.jl-9d4a7304-c3b4-5347-99a8-9cc862165b3e","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"kronecker-determinantal-point-processes","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/DeterminantalPointProcesses.jl-9d4a7304-c3b4-5347-99a8-9cc862165b3e","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"kronecker-determinantal-point-processes","repo_url":"https://github.com/alshedivat/DeterminantalPointProcesses.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"kronecker-determinantal-point-processes","repo_url":"https://github.com/theogf/DeterminantalPointProcesses.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"point-processes","task_name":"Point Processes"},{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}