{"title":"最优Bregman预测和Jensen等式","authors":"A. Banerjee, Xin Guo, Hui Wang","doi":"10.1109/ISIT.2004.1365205","DOIUrl":null,"url":null,"abstract":"This paper provides necessary and sufficient conditions for general loss functions under which the conditional expectation is the unique optimal predictor of a random variable. Further, using such loss functions, we give an exact characterization of the difference between the two sides of Jensen's inequality.","PeriodicalId":269907,"journal":{"name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","volume":" 86","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Optimal Bregman prediction and Jensen's equality\",\"authors\":\"A. Banerjee, Xin Guo, Hui Wang\",\"doi\":\"10.1109/ISIT.2004.1365205\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper provides necessary and sufficient conditions for general loss functions under which the conditional expectation is the unique optimal predictor of a random variable. Further, using such loss functions, we give an exact characterization of the difference between the two sides of Jensen's inequality.\",\"PeriodicalId\":269907,\"journal\":{\"name\":\"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.\",\"volume\":\" 86\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-10-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2004.1365205\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2004.1365205","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper provides necessary and sufficient conditions for general loss functions under which the conditional expectation is the unique optimal predictor of a random variable. Further, using such loss functions, we give an exact characterization of the difference between the two sides of Jensen's inequality.
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