{"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/a-randomized-algorithm-to-reduce-the-support","title":"A Randomized Algorithm to Reduce the Support of Discrete Measures","arxiv_id":"2006.01757","date":"2020-06-02","proceeding":"NeurIPS 2020 12","authors":["Francesco Cosentino","Harald Oberhauser","Alessandro Abate"],"abstract":"Given a discrete probability measure supported on $N$ atoms and a set of $n$ real-valued functions, there exists a probability measure that is supported on a subset of $n+1$ of the original $N$ atoms and has the same mean when integrated against each of the $n$ functions. If $ N \\gg n$ this results in a huge reduction of complexity. We give a simple geometric characterization of barycenters via negative cones and derive a randomized algorithm that computes this new measure by \"greedy geometric sampling\". We then study its properties, and benchmark it on synthetic and real-world data to show that it can be very beneficial in the $N\\gg n$ regime. A Python implementation is available at \\url{https://github.com/FraCose/Recombination_Random_Algos}.","url_abs":"https://arxiv.org/abs/2006.01757v2","url_pdf":"https://arxiv.org/pdf/2006.01757v2.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":"a-randomized-algorithm-to-reduce-the-support","repo_url":"https://github.com/FraCose/Recombination_Random_Algos","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2006.01757","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2006.01757"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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