Arnab Bhattacharyya, Sutanu Gayen, Kuldeep S. Meel, Dimitrios Myrisiotis, A. Pavan, N. V. Vinodchandran
{"title":"Total Variation Distance for Product Distributions is $\\#\\mathsf{P}$-Complete","authors":"Arnab Bhattacharyya, Sutanu Gayen, Kuldeep S. Meel, Dimitrios Myrisiotis, A. Pavan, N. V. Vinodchandran","doi":"arxiv-2405.08255","DOIUrl":null,"url":null,"abstract":"We show that computing the total variation distance between two product\ndistributions is $\\#\\mathsf{P}$-complete. This is in stark contrast with other\ndistance measures such as Kullback-Leibler, Chi-square, and Hellinger, which\ntensorize over the marginals leading to efficient algorithms.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.08255","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We show that computing the total variation distance between two product
distributions is $\#\mathsf{P}$-complete. This is in stark contrast with other
distance measures such as Kullback-Leibler, Chi-square, and Hellinger, which
tensorize over the marginals leading to efficient algorithms.
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