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arXiv · 1202.3399

Optimal error of query sets under the differentially-private matrix mechanism

Chao Li·Gerome Miklau
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Abstract

A common goal of privacy research is to release synthetic data that satisfies a formal privacy guarantee and can be used by an analyst in place of the original data. To achieve reasonable accuracy, a synthetic data set must be tuned to support a specified set of queries accurately, sacrificing fidelity for other queries. This work considers methods for producing synthetic data under differential privacy and investigates what makes a set of queries "easy" or "hard" to answer. We consider answering sets of linear counting queries using the matrix mechanism, a recent differentially-private mechanism that can reduce error by adding complex correlated noise adapted to a specified workload. Our main result is a novel lower bound on the minimum total error required to simultaneously release answers to a set of workload queries. The bound reveals that the hardness of a query workload is related to the spectral properties of the workload when it is represented in matrix form. The bound is most informative for $(\epsilon,\delta)$-differential privacy but also applies to $\epsilon$-differential privacy.

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Chao Li, Gerome Miklau. 2012-02-15. Optimal error of query sets under the differentially-private matrix mechanism. https://arxiv.org/abs/1202.3399

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