有限空间Kantorovich问题与表移动的MCMC

arXiv: Methodology Pub Date : 2020-02-24 DOI:10.1214/21-EJS1804

Giovanni Pistone, Fabio Rapallo, M. Rogantin

{"title":"有限空间Kantorovich问题与表移动的MCMC","authors":"Giovanni Pistone, Fabio Rapallo, M. Rogantin","doi":"10.1214/21-EJS1804","DOIUrl":null,"url":null,"abstract":"In Optimal Transport (OT) on a finite metric space, one defines a distance on the probability simplex that extends the distance on the ground space. The distance is the value of a Linear Programming (LP) problem on the set of nonegative-valued 2-way tables with assigned probability functions as margins. We apply to this case the methodology of moves from Algebraic Statistics (AS) and use it to derive an Monte Carlo Markov Chain solution algorithm.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"142 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Finite space Kantorovich problem with an MCMC of table moves\",\"authors\":\"Giovanni Pistone, Fabio Rapallo, M. Rogantin\",\"doi\":\"10.1214/21-EJS1804\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In Optimal Transport (OT) on a finite metric space, one defines a distance on the probability simplex that extends the distance on the ground space. The distance is the value of a Linear Programming (LP) problem on the set of nonegative-valued 2-way tables with assigned probability functions as margins. We apply to this case the methodology of moves from Algebraic Statistics (AS) and use it to derive an Monte Carlo Markov Chain solution algorithm.\",\"PeriodicalId\":186390,\"journal\":{\"name\":\"arXiv: Methodology\",\"volume\":\"142 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Methodology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/21-EJS1804\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Methodology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/21-EJS1804","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 3

摘要

在有限度量空间上的最优传输(OT)中，定义了概率单纯形上的距离，该距离扩展了地面空间上的距离。距离是一个线性规划(LP)问题在一组非负值的2路表上的值，这些表以指定的概率函数作为边界。我们将代数统计(AS)的移动方法应用于这种情况，并使用它来推导蒙特卡洛马尔可夫链解算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Finite space Kantorovich problem with an MCMC of table moves

In Optimal Transport (OT) on a finite metric space, one defines a distance on the probability simplex that extends the distance on the ground space. The distance is the value of a Linear Programming (LP) problem on the set of nonegative-valued 2-way tables with assigned probability functions as margins. We apply to this case the methodology of moves from Algebraic Statistics (AS) and use it to derive an Monte Carlo Markov Chain solution algorithm.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv: Methodology

自引率

0.00%

发文量

期刊最新文献

Revisiting Empirical Bayes Methods and Applications to Special Types of Data Flexible Bayesian modelling of concomitant covariate effects in mixture models A Critique of Differential Abundance Analysis, and Advocacy for an Alternative Post-Processing of MCMC Conditional variance estimator for sufficient dimension reduction