{"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/parallel-streaming-wasserstein-barycenters","title":"Parallel Streaming Wasserstein Barycenters","arxiv_id":"1705.07443","date":"2017-05-21","proceeding":"NeurIPS 2017 12","authors":["Matthew Staib","Sebastian Claici","Justin Solomon","Stefanie Jegelka"],"abstract":"Efficiently aggregating data from different sources is a challenging problem,\nparticularly when samples from each source are distributed differently. These\ndifferences can be inherent to the inference task or present for other reasons:\nsensors in a sensor network may be placed far apart, affecting their individual\nmeasurements. Conversely, it is computationally advantageous to split Bayesian\ninference tasks across subsets of data, but data need not be identically\ndistributed across subsets. One principled way to fuse probability\ndistributions is via the lens of optimal transport: the Wasserstein barycenter\nis a single distribution that summarizes a collection of input measures while\nrespecting their geometry. However, computing the barycenter scales poorly and\nrequires discretization of all input distributions and the barycenter itself.\nImproving on this situation, we present a scalable, communication-efficient,\nparallel algorithm for computing the Wasserstein barycenter of arbitrary\ndistributions. Our algorithm can operate directly on continuous input\ndistributions and is optimized for streaming data. Our method is even robust to\nnonstationary input distributions and produces a barycenter estimate that\ntracks the input measures over time. The algorithm is semi-discrete, needing to\ndiscretize only the barycenter estimate. To the best of our knowledge, we also\nprovide the first bounds on the quality of the approximate barycenter as the\ndiscretization becomes finer. Finally, we demonstrate the practical\neffectiveness of our method, both in tracking moving distributions on a sphere,\nas well as in a large-scale Bayesian inference task.","url_abs":"http://arxiv.org/abs/1705.07443v2","url_pdf":"http://arxiv.org/pdf/1705.07443v2.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":"parallel-streaming-wasserstein-barycenters","repo_url":"https://github.com/mstaib/stochastic-barycenter-code","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1705.07443","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}