Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman
{"title":"分离高斯分布混合学习的差分私有算法","authors":"Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman","doi":"10.1109/ITA50056.2020.9244945","DOIUrl":null,"url":null,"abstract":"Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particular, we give a differentially private analogue of the algorithm of Achlioptas and McSherry. Our algorithm has two key properties not achieved by prior work: (1) The algorithm’s sample complexity matches that of the corresponding non-private algorithm up to lower order terms in a wide range of parameters. (2) The algorithm does not require strong a priori bounds on the parameters of the mixture components.","PeriodicalId":137257,"journal":{"name":"2020 Information Theory and Applications Workshop (ITA)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"43","resultStr":"{\"title\":\"Differentially Private Algorithms for Learning Mixtures of Separated Gaussians\",\"authors\":\"Gautam Kamath, Or Sheffet, Vikrant Singhal, Jonathan Ullman\",\"doi\":\"10.1109/ITA50056.2020.9244945\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particular, we give a differentially private analogue of the algorithm of Achlioptas and McSherry. Our algorithm has two key properties not achieved by prior work: (1) The algorithm’s sample complexity matches that of the corresponding non-private algorithm up to lower order terms in a wide range of parameters. (2) The algorithm does not require strong a priori bounds on the parameters of the mixture components.\",\"PeriodicalId\":137257,\"journal\":{\"name\":\"2020 Information Theory and Applications Workshop (ITA)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"43\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2020 Information Theory and Applications Workshop (ITA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ITA50056.2020.9244945\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2020 Information Theory and Applications Workshop (ITA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITA50056.2020.9244945","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Differentially Private Algorithms for Learning Mixtures of Separated Gaussians
Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particular, we give a differentially private analogue of the algorithm of Achlioptas and McSherry. Our algorithm has two key properties not achieved by prior work: (1) The algorithm’s sample complexity matches that of the corresponding non-private algorithm up to lower order terms in a wide range of parameters. (2) The algorithm does not require strong a priori bounds on the parameters of the mixture components.