{"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/zonotope-hit-and-run-for-efficient-sampling","title":"Zonotope hit-and-run for efficient sampling from projection DPPs","arxiv_id":"1705.10498","date":"2017-05-30","proceeding":"ICML 2017 8","authors":["Guillaume Gautier","Rémi Bardenet","Michal Valko"],"abstract":"Determinantal point processes (DPPs) are distributions over sets of items\nthat model diversity using kernels. Their applications in machine learning\ninclude summary extraction and recommendation systems. Yet, the cost of\nsampling from a DPP is prohibitive in large-scale applications, which has\ntriggered an effort towards efficient approximate samplers. We build a novel\nMCMC sampler that combines ideas from combinatorial geometry, linear\nprogramming, and Monte Carlo methods to sample from DPPs with a fixed sample\ncardinality, also called projection DPPs. Our sampler leverages the ability of\nthe hit-and-run MCMC kernel to efficiently move across convex bodies. Previous\ntheoretical results yield a fast mixing time of our chain when targeting a\ndistribution that is close to a projection DPP, but not a DPP in general. Our\nempirical results demonstrate that this extends to sampling projection DPPs,\ni.e., our sampler is more sample-efficient than previous approaches which in\nturn translates to faster convergence when dealing with costly-to-evaluate\nfunctions, such as summary extraction in our experiments.","url_abs":"http://arxiv.org/abs/1705.10498v2","url_pdf":"http://arxiv.org/pdf/1705.10498v2.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":"zonotope-hit-and-run-for-efficient-sampling","repo_url":"https://github.com/guilgautier/DPPy","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"diversity","task_name":"Diversity"},{"task_slug":"point-processes","task_name":"Point Processes"},{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}