{"title":"Rényi Entropies of Projections","authors":"P. Harremoës, C. Vignat","doi":"10.1109/ISIT.2006.261750","DOIUrl":null,"url":null,"abstract":"In this paper we are interested in n-dimensional uniform distributions on a triangle and a sphere. We show that their marginal distributions are maximizers of Renyi entropy under a constraint of variance and expectation in the respective cases of the sphere and of the triangle. Moreover, using an example, we show that a distribution on a triangle with (uniform) maximum entropy marginals may have an arbitrary small entropy. As a last result, we address the asymptotic behavior of these results and provide a link to the de Finetti theorem","PeriodicalId":115298,"journal":{"name":"2006 IEEE International Symposium on Information Theory","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 IEEE International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2006.261750","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper we are interested in n-dimensional uniform distributions on a triangle and a sphere. We show that their marginal distributions are maximizers of Renyi entropy under a constraint of variance and expectation in the respective cases of the sphere and of the triangle. Moreover, using an example, we show that a distribution on a triangle with (uniform) maximum entropy marginals may have an arbitrary small entropy. As a last result, we address the asymptotic behavior of these results and provide a link to the de Finetti theorem
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