{"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/optimized-algorithms-to-sample-determinantal","title":"Optimized Algorithms to Sample Determinantal Point Processes","arxiv_id":"1802.08471","date":"2018-02-23","proceeding":null,"authors":["Nicolas Tremblay","Simon Barthelme","Pierre-Olivier Amblard"],"abstract":"In this technical report, we discuss several sampling algorithms for\nDeterminantal Point Processes (DPP). DPPs have recently gained a broad interest\nin the machine learning and statistics literature as random point processes\nwith negative correlation, i.e., ones that can generate a \"diverse\" sample from\na set of items. They are parametrized by a matrix $\\mathbf{L}$, called\n$L$-ensemble, that encodes the correlations between items. The standard\nsampling algorithm is separated in three phases: 1/~eigendecomposition of\n$\\mathbf{L}$, 2/~an eigenvector sampling phase where $\\mathbf{L}$'s\neigenvectors are sampled independently via a Bernoulli variable parametrized by\ntheir associated eigenvalue, 3/~a Gram-Schmidt-type orthogonalisation procedure\nof the sampled eigenvectors.\n  In a naive implementation, the computational cost of the third step is on\naverage $\\mathcal{O}(N\\mu^3)$ where $\\mu$ is the average number of samples of\nthe DPP. We give an algorithm which runs in $\\mathcal{O}(N\\mu^2)$ and is\nextremely simple to implement. If memory is a constraint, we also describe a\ndual variant with reduced memory costs. In addition, we discuss implementation\ndetails often missing in the literature.","url_abs":"http://arxiv.org/abs/1802.08471v1","url_pdf":"http://arxiv.org/pdf/1802.08471v1.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":"optimized-algorithms-to-sample-determinantal","repo_url":"https://github.com/dahtah/DPP.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"LGPL-3.0"}},{"paper_slug":"optimized-algorithms-to-sample-determinantal","repo_url":"https://github.com/dahtah/determinantal.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"LGPL-3.0"}}],"tasks":[{"task_slug":"point-processes","task_name":"Point Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}