{"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/high-performance-sampling-of-generic","title":"High-performance sampling of generic Determinantal Point Processes","arxiv_id":"1905.00165","date":"2019-05-01","proceeding":null,"authors":["Jack Poulson"],"abstract":"Determinantal Point Processes (DPPs) were introduced by Macchi as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a recommender system. The standard sampling scheme for finite DPPs is a spectral decomposition followed by an equivalent of a randomly diagonally-pivoted Cholesky factorization of an orthogonal projection, which is only applicable to Hermitian kernels and has an expensive setup cost. Researchers have begun to connect DPP sampling to $LDL^H$ factorizations as a means of avoiding the initial spectral decomposition, but existing approaches have only outperformed the spectral decomposition approach in special circumstances, where the number of kept modes is a small percentage of the ground set size. This article proves that trivial modifications of $LU$ and $LDL^H$ factorizations yield efficient direct sampling schemes for non-Hermitian and Hermitian DPP kernels, respectively. Further, it is experimentally shown that even dynamically-scheduled, shared-memory parallelizations of high-performance dense and sparse-direct factorizations can be trivially modified to yield DPP sampling schemes with essentially identical performance. The software developed as part of this research, Catamari, https://hodgestar.com/catamari, is released under the Mozilla Public License v2.0. It contains header-only, C++14 plus OpenMP 4.0 implementations of dense and sparse-direct, Hermitian and non-Hermitian DPP samplers.","url_abs":"http://arxiv.org/abs/1905.00165v2","url_pdf":"http://arxiv.org/pdf/1905.00165v2.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":"high-performance-sampling-of-generic","repo_url":"https://gitlab.com/hodge_star/catamari","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=1905.00165","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}