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Efficient Algorithm for Privately Releasing Smooth Queries
Ziteng Wang · Kai Fan · Jiaqi Zhang · Liwei Wang

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor
We study differentially private mechanisms for answering \emph{smooth} queries on databases consisting of data points in $\mathbb{R}^d$. A $K$-smooth query is specified by a function whose partial derivatives up to order $K$ are all bounded. We develop an $\epsilon$-differentially private mechanism which for the class of $K$-smooth queries has accuracy $O (\left(\frac{1}{n}\right)^{\frac{K}{2d+K}}/\epsilon)$. The mechanism first outputs a summary of the database. To obtain an answer of a query, the user runs a public evaluation algorithm which contains no information of the database. Outputting the summary runs in time $O(n^{1+\frac{d}{2d+K}})$, and the evaluation algorithm for answering a query runs in time $\tilde O (n^{\frac{d+2+\frac{2d}{K}}{2d+K}} )$. Our mechanism is based on $L_{\infty}$-approximation of (transformed) smooth functions by low degree even trigonometric polynomials with small and efficiently computable coefficients.

Author Information

Ziteng Wang
Kai Fan (Peking University)
Jiaqi Zhang (Peking University)
Liwei Wang (Peking University)

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