Differentially Private Data Releasing for Smooth Queries with Synthetic Database Output
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We consider accurately answering smooth queries while preserving differential privacy. A query is said to be K-smooth if it is specified by a function defined on [-1,1]^d whose partial derivatives up to order K are all bounded. We develop an ϵ-differentially private mechanism for the class of K-smooth queries. The major advantage of the algorithm is that it outputs a synthetic database. In real applications, a synthetic database output is appealing. Our mechanism achieves an accuracy of O (n^-K/2d+K/ϵ ), and runs in polynomial time. We also generalize the mechanism to preserve (ϵ, δ)-differential privacy with slightly improved accuracy. Extensive experiments on benchmark datasets demonstrate that the mechanisms have good accuracy and are efficient.
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