{"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/one-nearest-neighbor-search-is-all-you-need","title":"Minimax Optimal Algorithms with Fixed-$k$-Nearest Neighbors","arxiv_id":"2202.02464","date":"2022-02-05","proceeding":null,"authors":["J. Jon Ryu","Young-Han Kim"],"abstract":"This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-$k$ nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into smaller groups, where the $k$-NNs are found for a query point with respect to each subset of data. We propose \\emph{optimal} rules to aggregate the fixed-$k$-NN information for classification, regression, and density estimation that achieve minimax optimal rates for the respective problems. We show that the distributed algorithm with a fixed $k$ over a sufficiently large number of groups attains a minimax optimal error rate up to a multiplicative logarithmic factor under some regularity conditions. Roughly speaking, distributed $k$-NN rules with $M$ groups has a performance comparable to the standard $\\Theta(kM)$-NN rules even for fixed $k$.","url_abs":"https://arxiv.org/abs/2202.02464v3","url_pdf":"https://arxiv.org/pdf/2202.02464v3.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":"one-nearest-neighbor-search-is-all-you-need","repo_url":"https://github.com/jongharyu/split-knn-rules","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}