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	Differentially Private Data Releasing for Smooth Queries
	Wang, Ziteng ; Jin, Chi ; Fan, Kai ; Zhang, Jiaqi ; Huang, Junliang ; Zhong, Yiqiao ; Wang, Liwei
	2016
关键词	differential privacy smooth queries synthetic dataset ALGORITHMS COMPLEXITY
英文摘要	In the past few years, differential privacy has become a standard concept in the area of privacy. One of the most important problems in this field is to answer queries while preserving differential privacy. In spite of extensive studies, most existing work on differentially private query answering assumes the data are discrete (i.e., in {0, 1}(d)) and focuses on queries induced by Boolean functions. In real applications however, continuous data are at least as common as binary data. Thus, in this work we explore a less studied topic, namely, differential privately query answering for continuous data with continuous function. As a first step towards the continuous case, we study a natural class of linear queries on continuous data which we refer to as smooth queries. A linear query is said to be K-smooth if it is specified by a function de fined on [1; 1](d) whose partial derivatives up to order K are all bounded. We develop two is an element of-differentially private mechanisms which are able to answer all smooth queries. The first mechanism outputs a summary of the database and can then give answers to the queries. The second mechanism is an improvement of the first one and it outputs a synthetic database. The two mechanisms both achieve an accuracy of O(n-K/2d+K/is an element of). Here we assume that the dimension d is a constant. It turns out that even in this parameter setting (which is almost trivial in the discrete case), using existing discrete mechanisms to answer the smooth queries is difficult and requires more noise. Our mechanisms are based on L-infinity-approximation of (transformed) smooth functions by low-degree even trigonometric polynomials with uniformly bounded coefficients. We also develop practically efficient variants of the mechanisms with promising experimental results.; National Basic Research Program of China (973 Program) [2015CB352502]; NSFC [61573026, 61222307]; IBM Faculty Award; Microsoft Research Asia; SCI(E); ARTICLE; WANGZT2012@GMAIL.COM; CHIJIN@CS.BERKELEY.EDU; KAI.FAN@DUKE.EDU; ZHANGJQ@CIS.PKU.EDU.CN; HUANGJUNLIANG@PKU.EDU.CN; YIQIAOZHONG@PKU.EDU.CN; WANGLW@CIS.PKU.EDU.CN; 1-42; 17
语种	英语
出处	SCI
出版者	JOURNAL OF MACHINE LEARNING RESEARCH
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/459087]
专题	数学科学学院 信息科学技术学院
推荐引用方式 GB/T 7714	Wang, Ziteng,Jin, Chi,Fan, Kai,et al. Differentially Private Data Releasing for Smooth Queries. 2016-01-01.

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