{"title":"Marginal Independence Models","authors":"T. Boege, Sonja Petrovi'c, B. Sturmfels","doi":"10.1145/3476446.3536193","DOIUrl":null,"url":null,"abstract":"We impose rank one constraints on marginalizations of a tensor, given by a simplicial complex. Following work of Kirkup and Sullivant, such marginal independence models can be made toric by a linear change of coordinates. We study their toric ideals, with emphasis on random graph models and independent set polytopes of matroids. We develop the numerical algebra of parameter estimation, using both Euclidean distance and maximum likelihood, and we present a comprehensive database of small models.","PeriodicalId":130499,"journal":{"name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3476446.3536193","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
We impose rank one constraints on marginalizations of a tensor, given by a simplicial complex. Following work of Kirkup and Sullivant, such marginal independence models can be made toric by a linear change of coordinates. We study their toric ideals, with emphasis on random graph models and independent set polytopes of matroids. We develop the numerical algebra of parameter estimation, using both Euclidean distance and maximum likelihood, and we present a comprehensive database of small models.
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