Differentially Private Data Releasing for Smooth Queries with Synthetic Database Output
This work addresses privacy-preserving data analysis for applications requiring synthetic data outputs, representing an incremental improvement with specific gains.
The paper tackles the problem of accurately answering smooth queries under differential privacy by outputting a synthetic database, achieving an accuracy of O(n^{-K/(2d+K)}/ε) and running in polynomial time.
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 $O (n^{-\frac{K}{2d+K}}/ε)$, 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.