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We consider the problem of differentially private query release through asynthetic database approach. Departing from the existing approaches thatrequire the query set to be specified in advance, we advocate to devisequery-set independent mechanisms, with an ambitious goal of providing accurateanswers, while meeting the privacy constraints, for all queries in a generalquery class. Specifically, a differentially private mechanism is constructed to"encode" rich stochastic structure into the synthetic database, and"customized" companion estimators are then derived to provide accurate answersby making use of all available information, including the mechanism (which ispublic information) and the query functions. Accordingly, the distortion underthe best of this kind of mechanisms at the worst-case query in a general queryclass, so called the minimax distortion, provides a fundamentalcharacterization of differentially private query release.  For the general class of statistical queries, we prove that with thesquared-error distortion measure, the minimax distortion is $O(1/n)$ byderiving asymptotically tight upper and lower bounds in the regime that thedatabase size $n$ goes to infinity. The upper bound is achievable by amechanism $\mathcal{E}$ and its corresponding companion estimators, whichpoints directly to the feasibility of the proposed approach in large databases.We further evaluate the mechanism $\mathcal{E}$ and the companion estimatorsthrough experiments on real datasets from Netflix and Facebook. Experimentalresults show improvement over the state-of-art MWEM algorithm and verify thescaling behavior $O(1/n)$ of the minimax distortion.

A Minimax Distortion View of Differentially Private Query Release