极大似然度，完全二次函数，和*-作用

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-01-01 DOI:10.1137/20M1335960

M. Michałek, Leonid Monin, Jaroslaw A. Wisniewski

{"title":"极大似然度，完全二次函数，和*-作用","authors":"M. Michałek, Leonid Monin, Jaroslaw A. Wisniewski","doi":"10.1137/20M1335960","DOIUrl":null,"url":null,"abstract":"We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on the variety of complete quadrics. This allows us to provide an explicit, basic, albeit of high computational complexity, formula for the ML-degree. The variety of complete quadrics is an exact analog for symmetric matrices of the permutohedron variety for the diagonal matrices.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":"{\"title\":\"Maximum Likelihood Degree, Complete Quadrics, and ℂ*-Action\",\"authors\":\"M. Michałek, Leonid Monin, Jaroslaw A. Wisniewski\",\"doi\":\"10.1137/20M1335960\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on the variety of complete quadrics. This allows us to provide an explicit, basic, albeit of high computational complexity, formula for the ML-degree. The variety of complete quadrics is an exact analog for symmetric matrices of the permutohedron variety for the diagonal matrices.\",\"PeriodicalId\":48489,\"journal\":{\"name\":\"SIAM Journal on Applied Algebra and Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Applied Algebra and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/20M1335960\",\"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/10.1137/20M1335960","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: 24

摘要

本文研究了代数统计中线性浓度模型的最大似然度。我们把它与各种完全二次曲线的交点问题联系起来。这允许我们为ml度提供一个明确的、基本的(尽管计算复杂度很高)公式。完全二次曲面的变化是对角矩阵的复面体变化的对称矩阵的精确类比。

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

Maximum Likelihood Degree, Complete Quadrics, and ℂ*-Action

We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on the variety of complete quadrics. This allows us to provide an explicit, basic, albeit of high computational complexity, formula for the ML-degree. The variety of complete quadrics is an exact analog for symmetric matrices of the permutohedron variety for the diagonal matrices.

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