{"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/tsallis-regularized-optimal-transport-and","title":"Tsallis Regularized Optimal Transport and Ecological Inference","arxiv_id":"1609.04495","date":"2016-09-15","proceeding":null,"authors":["Boris Muzellec","Richard Nock","Giorgio Patrini","Frank Nielsen"],"abstract":"Optimal transport is a powerful framework for computing distances between\nprobability distributions. We unify the two main approaches to optimal\ntransport, namely Monge-Kantorovitch and Sinkhorn-Cuturi, into what we define\nas Tsallis regularized optimal transport (\\trot). \\trot~interpolates a rich\nfamily of distortions from Wasserstein to Kullback-Leibler, encompassing as\nwell Pearson, Neyman and Hellinger divergences, to name a few. We show that\nmetric properties known for Sinkhorn-Cuturi generalize to \\trot, and provide\nefficient algorithms for finding the optimal transportation plan with formal\nconvergence proofs. We also present the first application of optimal transport\nto the problem of ecological inference, that is, the reconstruction of joint\ndistributions from their marginals, a problem of large interest in the social\nsciences. \\trot~provides a convenient framework for ecological inference by\nallowing to compute the joint distribution --- that is, the optimal\ntransportation plan itself --- when side information is available, which is\n\\textit{e.g.} typically what census represents in political science.\nExperiments on data from the 2012 US presidential elections display the\npotential of \\trot~in delivering a faithful reconstruction of the joint\ndistribution of ethnic groups and voter preferences.","url_abs":"http://arxiv.org/abs/1609.04495v1","url_pdf":"http://arxiv.org/pdf/1609.04495v1.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":"tsallis-regularized-optimal-transport-and","repo_url":"https://github.com/BorisMuzellec/TROT","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"tsallis-regularized-optimal-transport-and","repo_url":"https://github.com/MindSpore-scientific-2/code-2/tree/main/TSA_mindspore","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1609.04495","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1609.04495"}},"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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