Joint Mixability and Notions of Negative Dependence

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-29 DOI:10.1287/moor.2022.0121

Takaaki Koike, Liyuan Lin, Ruodu Wang

{"title":"Joint Mixability and Notions of Negative Dependence","authors":"Takaaki Koike, Liyuan Lin, Ruodu Wang","doi":"10.1287/moor.2022.0121","DOIUrl":null,"url":null,"abstract":"A joint mix (JM) is a random vector with a constant component-wise sum. The dependence structure of a joint mix minimizes some common objectives, such as the variance of the component-wise sum, and it is regarded as a concept of extremal negative dependence. In this paper, we explore the connection between the joint mix structure and popular notions of negative dependence in statistics, such as negative correlation dependence, negative orthant dependence, and negative association. A joint mix is not always negatively dependent in any of these senses, but some natural classes of joint mixes are. We derive various necessary and sufficient conditions for a joint mix to be negatively dependent and study the compatibility of these notions. For identical marginal distributions, we show that a negatively dependent joint mix solves a multimarginal optimal transport problem for quadratic cost under a novel setting of uncertainty. Analysis of this optimal transport problem with heterogeneous marginals reveals a trade-off between negative dependence and the joint mix structure.Funding: T. Koike was supported by the Japan Society for the Promotion of Science [Grant JSPS KAKENHI JP21K13275]. R. Wang acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2018-03823 and RGPAS-2018-522590].","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1287/moor.2022.0121","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

A joint mix (JM) is a random vector with a constant component-wise sum. The dependence structure of a joint mix minimizes some common objectives, such as the variance of the component-wise sum, and it is regarded as a concept of extremal negative dependence. In this paper, we explore the connection between the joint mix structure and popular notions of negative dependence in statistics, such as negative correlation dependence, negative orthant dependence, and negative association. A joint mix is not always negatively dependent in any of these senses, but some natural classes of joint mixes are. We derive various necessary and sufficient conditions for a joint mix to be negatively dependent and study the compatibility of these notions. For identical marginal distributions, we show that a negatively dependent joint mix solves a multimarginal optimal transport problem for quadratic cost under a novel setting of uncertainty. Analysis of this optimal transport problem with heterogeneous marginals reveals a trade-off between negative dependence and the joint mix structure.Funding: T. Koike was supported by the Japan Society for the Promotion of Science [Grant JSPS KAKENHI JP21K13275]. R. Wang acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2018-03823 and RGPAS-2018-522590].

查看原文本刊更多论文

联合混合性和负相关概念

联合混合（JM）是一种具有恒定分量和的随机向量。联合混合的依赖结构能使一些常见目标（如分量和的方差）最小化，它被视为极端负依赖的概念。在本文中，我们将探讨联合混合结构与统计学中流行的负依赖性概念（如负相关依赖性、负正相关依赖性和负关联性）之间的联系。联合混合结构并不总是这些意义上的负依赖性，但有些自然类的联合混合结构是负依赖性的。我们推导了联合混合负相关的各种必要条件和充分条件，并研究了这些概念的兼容性。在边际分布相同的情况下，我们证明了负相关联合组合可以解决一个新颖的不确定性环境下二次成本的多边际最优运输问题。对这个具有异质性边际分布的最优运输问题的分析揭示了负依赖性与联合混合结构之间的权衡：T. Koike 得到了日本学术振兴会的资助[JSPS KAKENHI JP21K13275]。R. Wang 感谢加拿大自然科学与工程研究理事会 [Grants RGPIN-2018-03823 and RGPAS-2018-522590] 的资助。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.