{"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/exact-sampling-of-determinantal-point-1","title":"Exact sampling of determinantal point processes with sublinear time preprocessing","arxiv_id":"1905.13476","date":"2019-05-31","proceeding":"NeurIPS 2019 12","authors":["Michał Dereziński","Daniele Calandriello","Michal Valko"],"abstract":"We study the complexity of sampling from a distribution over all index subsets of the set $\\{1,...,n\\}$ with the probability of a subset $S$ proportional to the determinant of the submatrix $\\mathbf{L}_S$ of some $n\\times n$ p.s.d. matrix $\\mathbf{L}$, where $\\mathbf{L}_S$ corresponds to the entries of $\\mathbf{L}$ indexed by $S$. Known as a determinantal point process, this distribution is used in machine learning to induce diversity in subset selection. In practice, we often wish to sample multiple subsets $S$ with small expected size $k = E[|S|] \\ll n$ from a very large matrix $\\mathbf{L}$, so it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). For this purpose, we propose a new algorithm which, given access to $\\mathbf{L}$, samples exactly from a determinantal point process while satisfying the following two properties: (1) its preprocessing cost is $n \\cdot \\text{poly}(k)$, i.e., sublinear in the size of $\\mathbf{L}$, and (2) its sampling cost is $\\text{poly}(k)$, i.e., independent of the size of $\\mathbf{L}$. Prior to our results, state-of-the-art exact samplers required $O(n^3)$ preprocessing time and sampling time linear in $n$ or dependent on the spectral properties of $\\mathbf{L}$. We also give a reduction which allows using our algorithm for exact sampling from cardinality constrained determinantal point processes with $n\\cdot\\text{poly}(k)$ time preprocessing.","url_abs":"https://arxiv.org/abs/1905.13476v2","url_pdf":"https://arxiv.org/pdf/1905.13476v2.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":"exact-sampling-of-determinantal-point-1","repo_url":"https://github.com/LCSL/dpp-vfx","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"exact-sampling-of-determinantal-point-1","repo_url":"https://github.com/guilgautier/DPPy","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"point-processes","task_name":"Point Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1905.13476","atlas_url":"https://app.syntology.ai/?focus=1905.13476","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}