Efficient Batch Query Answering Under Differential Privacy

Differential privacy is a rigorous privacy condition achieved by randomizing query answers. This paper develops efficient algorithms for answering multiple queries under differential privacy with low error. We pursue this goal by advancing a recent approach called the matrix mechanism, which generalizes standard differentially private mechanisms. This new mechanism works by first answering a different set of queries (a strategy) and then inferring the answers to the desired workload of queries. Although a few strategies are known to work well on specific workloads, finding the strategy which minimizes error on an arbitrary workload is intractable. We prove a new lower bound on the optimal error of this mechanism, and we propose an efficient algorithm that approaches this bound for a wide range of workloads.Comment: 6 figues, 22 page

An Adaptive Mechanism for Accurate Query Answering under Differential Privacy

We propose a novel mechanism for answering sets of count- ing queries under differential privacy. Given a workload of counting queries, the mechanism automatically selects a different set of "strategy" queries to answer privately, using those answers to derive answers to the workload. The main algorithm proposed in this paper approximates the optimal strategy for any workload of linear counting queries. With no cost to the privacy guarantee, the mechanism improves significantly on prior approaches and achieves near-optimal error for many workloads, when applied under (\epsilon, \delta)-differential privacy. The result is an adaptive mechanism which can help users achieve good utility without requiring that they reason carefully about the best formulation of their task.Comment: VLDB2012. arXiv admin note: substantial text overlap with arXiv:1103.136

Linear and Range Counting under Metric-based Local Differential Privacy

Local differential privacy (LDP) enables private data sharing and analytics without the need for a trusted data collector. Error-optimal primitives (for, e.g., estimating means and item frequencies) under LDP have been well studied. For analytical tasks such as range queries, however, the best known error bound is dependent on the domain size of private data, which is potentially prohibitive. This deficiency is inherent as LDP protects the same level of indistinguishability between any pair of private data values for each data downer. In this paper, we utilize an extension of $\epsilon$-LDP called Metric-LDP or $E$-LDP, where a metric $E$ defines heterogeneous privacy guarantees for different pairs of private data values and thus provides a more flexible knob than $\epsilon$ does to relax LDP and tune utility-privacy trade-offs. We show that, under such privacy relaxations, for analytical workloads such as linear counting, multi-dimensional range counting queries, and quantile queries, we can achieve significant gains in utility. In particular, for range queries under $E$-LDP where the metric $E$ is the $L^1$-distance function scaled by $\epsilon$, we design mechanisms with errors independent on the domain sizes; instead, their errors depend on the metric $E$, which specifies in what granularity the private data is protected. We believe that the primitives we design for $E$-LDP will be useful in developing mechanisms for other analytical tasks, and encourage the adoption of LDP in practice

Distributed Private Heavy Hitters

In this paper, we give efficient algorithms and lower bounds for solving the heavy hitters problem while preserving differential privacy in the fully distributed local model. In this model, there are n parties, each of which possesses a single element from a universe of size N. The heavy hitters problem is to find the identity of the most common element shared amongst the n parties. In the local model, there is no trusted database administrator, and so the algorithm must interact with each of the $n$ parties separately, using a differentially private protocol. We give tight information-theoretic upper and lower bounds on the accuracy to which this problem can be solved in the local model (giving a separation between the local model and the more common centralized model of privacy), as well as computationally efficient algorithms even in the case where the data universe N may be exponentially large