Optimizing linear counting queries under differential privacy

Abstract

N.B. This is the full version of the conference paper published as [12]. This version includes an Appendix with proofs and additional results, and corrects a few typographical errors discovered after publication. It also adds an improvement in the error bounds achieved under ( , δ)-differential privacy, included as Theorem 5. ABSTRACTDifferential privacy is a robust privacy standard that has been successfully applied to a range of data analysis tasks. But despite much recent work, optimal strategies for answering a collection of related queries are not known.We propose the matrix mechanism, a new algorithm for answering a workload of predicate counting queries. Given a workload, the mechanism requests answers to a different set of queries, called a query strategy, which are answered using the standard Laplace mechanism. Noisy answers to the workload queries are then derived from the noisy answers to the strategy queries. This two stage process can result in a more complex correlated noise distribution that preserves differential privacy but increases accuracy.We provide a formal analysis of the error of query answers produced by the mechanism and investigate the problem of computing the optimal query strategy in support of a given workload. We show this problem can be formulated as a rank-constrained semidefinite program. Finally, we analyze two seemingly distinct techniques, whose similar behavior is explained by viewing them as instances of the matrix mechanism.

Differentially Private Histogram Publication

“…Thus, a query executer can provide the users more precise results by querying the DPcomplaint histogram published by the StructureFirst method. Among the existing approaches, the ones most related to ours are by Blum et al [19], Hay et al [6], Xiao et al [8], and Li et al [7]. Specifically, Blum et al [19] propose to construct one-dimensional histograms by dividing the input counts into several bins, such that the sum of counts in each bin is roughly the same.…”

“…Li et al [7] propose an approach that generalizes both Hay et al's and Xiao et al's techniques in the sense that it can achieve optimal noise variance bound for a large spectrum of query workloads. In contrast, Hay et al's and Xiao et al's techniques only optimizes the accuracy of range count queries.…”

Differentially Private Filtering

“…If the dynamics (9) are not stable, the linear filter design approach presented in the previous paragraph is not valid. To handle this case, we can further restrict the class of filters.…”

“…Most work related to privacy is concerned with the analysis of static databases [5], [7]- [9], whereas cyber-physical systems clearly emphasize the need for mechanisms working with dynamic, time-varying data streams. Recently, the problem of releasing differentially private statistics when the input data takes the form of a binary stream has been considered in [10]- [12].…”

DPCube: Releasing Differentially Private Data Cubes for Health Information

“…Non-interactive data release with differential privacy has been recently studied with hardness results obtained and it remains an open problem to find efficient algorithms for many domains [5]. A few recent works [12], [17], [10] considered the problem of releasing data for general predicate counting queries. While promising, the query strategies being used are data-oblivious in that they are determined by the query workload, a wavelet matrix, or a hierarchical matrix without taking into consideration the underlying data.…”