稀疏多项式系统的最大似然度

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-05-16 DOI:10.1137/21m1422550

J. Lindberg, Nathan Nicholson, J. Rodriguez, Zinan Wang

{"title":"稀疏多项式系统的最大似然度","authors":"J. Lindberg, Nathan Nicholson, J. Rodriguez, Zinan Wang","doi":"10.1137/21m1422550","DOIUrl":null,"url":null,"abstract":"We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of critical points of the likelihood function restricted to the model. We prove the maximum likelihood degree of a sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2021-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The Maximum Likelihood Degree of Sparse Polynomial Systems\",\"authors\":\"J. Lindberg, Nathan Nicholson, J. Rodriguez, Zinan Wang\",\"doi\":\"10.1137/21m1422550\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of critical points of the likelihood function restricted to the model. We prove the maximum likelihood degree of a sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.\",\"PeriodicalId\":48489,\"journal\":{\"name\":\"SIAM Journal on Applied Algebra and Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2021-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Applied Algebra and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/21m1422550\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Algebra and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/21m1422550","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 3

摘要

我们考虑由具有一般系数的稀疏多项式系统的公共解集产生的统计模型。最大似然度计算模型限定的似然函数的临界点的个数。我们证明了一个稀疏多项式系统的最大似然度是由它的牛顿多体决定的，并且等于一个相关的拉格朗日方程组的混合体积。

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

The Maximum Likelihood Degree of Sparse Polynomial Systems

We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of critical points of the likelihood function restricted to the model. We prove the maximum likelihood degree of a sparse polynomial system is determined by its Newton polytopes and equals the mixed volume of a related Lagrange system of equations.

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