{"title":"平方格拉斯曼的似然几何","authors":"Hannah Friedman","doi":"arxiv-2409.03730","DOIUrl":null,"url":null,"abstract":"We study projection determinantal point processes and their connection to the\nsquared Grassmannian. We prove that the log-likelihood function of this\nstatistical model has $(n - 1)!/2$ critical points, all of which are real and\npositive, thereby settling a conjecture of Devriendt, Friedman, Reinke, and\nSturmfels.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"35 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Likelihood Geometry of the Squared Grassmannian\",\"authors\":\"Hannah Friedman\",\"doi\":\"arxiv-2409.03730\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study projection determinantal point processes and their connection to the\\nsquared Grassmannian. We prove that the log-likelihood function of this\\nstatistical model has $(n - 1)!/2$ critical points, all of which are real and\\npositive, thereby settling a conjecture of Devriendt, Friedman, Reinke, and\\nSturmfels.\",\"PeriodicalId\":501379,\"journal\":{\"name\":\"arXiv - STAT - Statistics Theory\",\"volume\":\"35 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - STAT - Statistics Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.03730\",\"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 - STAT - Statistics Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.03730","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study projection determinantal point processes and their connection to the
squared Grassmannian. We prove that the log-likelihood function of this
statistical model has $(n - 1)!/2$ critical points, all of which are real and
positive, thereby settling a conjecture of Devriendt, Friedman, Reinke, and
Sturmfels.
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