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

Optimizing Batch Linear Queries under Exact and Approximate Differential Privacy

Differential privacy is a promising privacy-preserving paradigm for statistical query processing over sensitive data. It works by injecting random noise into each query result, such that it is provably hard for the adversary to infer the presence or absence of any individual record from the published noisy results. The main objective in differentially private query processing is to maximize the accuracy of the query results, while satisfying the privacy guarantees. Previous work, notably \cite{LHR+10}, has suggested that with an appropriate strategy, processing a batch of correlated queries as a whole achieves considerably higher accuracy than answering them individually. However, to our knowledge there is currently no practical solution to find such a strategy for an arbitrary query batch; existing methods either return strategies of poor quality (often worse than naive methods) or require prohibitively expensive computations for even moderately large domains. Motivated by this, we propose low-rank mechanism (LRM), the first practical differentially private technique for answering batch linear queries with high accuracy. LRM works for both exact (i.e., $\epsilon$-) and approximate (i.e., ($\epsilon$, $\delta$)-) differential privacy definitions. We derive the utility guarantees of LRM, and provide guidance on how to set the privacy parameters given the user's utility expectation. Extensive experiments using real data demonstrate that our proposed method consistently outperforms state-of-the-art query processing solutions under differential privacy, by large margins.Comment: ACM Transactions on Database Systems (ACM TODS). arXiv admin note: text overlap with arXiv:1212.230

Convex Optimization for Linear Query Processing under Approximate Differential Privacy

Differential privacy enables organizations to collect accurate aggregates over sensitive data with strong, rigorous guarantees on individuals' privacy. Previous work has found that under differential privacy, computing multiple correlated aggregates as a batch, using an appropriate \emph{strategy}, may yield higher accuracy than computing each of them independently. However, finding the best strategy that maximizes result accuracy is non-trivial, as it involves solving a complex constrained optimization program that appears to be non-linear and non-convex. Hence, in the past much effort has been devoted in solving this non-convex optimization program. Existing approaches include various sophisticated heuristics and expensive numerical solutions. None of them, however, guarantees to find the optimal solution of this optimization problem. This paper points out that under ($\epsilon$, $\delta$)-differential privacy, the optimal solution of the above constrained optimization problem in search of a suitable strategy can be found, rather surprisingly, by solving a simple and elegant convex optimization program. Then, we propose an efficient algorithm based on Newton's method, which we prove to always converge to the optimal solution with linear global convergence rate and quadratic local convergence rate. Empirical evaluations demonstrate the accuracy and efficiency of the proposed solution.Comment: to appear in ACM SIGKDD 201

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

Low-Rank Mechanism: Optimizing Batch Queries under Differential Privacy

Differential privacy is a promising privacy-preserving paradigm for statistical query processing over sensitive data. It works by injecting random noise into each query result, such that it is provably hard for the adversary to infer the presence or absence of any individual record from the published noisy results. The main objective in differentially private query processing is to maximize the accuracy of the query results, while satisfying the privacy guarantees. Previous work, notably the matrix mechanism, has suggested that processing a batch of correlated queries as a whole can potentially achieve considerable accuracy gains, compared to answering them individually. However, as we point out in this paper, the matrix mechanism is mainly of theoretical interest; in particular, several inherent problems in its design limit its accuracy in practice, which almost never exceeds that of naive methods. In fact, we are not aware of any existing solution that can effectively optimize a query batch under differential privacy. Motivated by this, we propose the Low-Rank Mechanism (LRM), the first practical differentially private technique for answering batch queries with high accuracy, based on a low rank approximation of the workload matrix. We prove that the accuracy provided by LRM is close to the theoretical lower bound for any mechanism to answer a batch of queries under differential privacy. Extensive experiments using real data demonstrate that LRM consistently outperforms state-of-the-art query processing solutions under differential privacy, by large margins.Comment: VLDB201

Approximate Data Analytics Systems

Today, most modern online services make use of big data analytics systems to extract useful information from the raw digital data. The data normally arrives as a continuous data stream at a high speed and in huge volumes. The cost of handling this massive data can be significant. Providing interactive latency in processing the data is often impractical due to the fact that the data is growing exponentially and even faster than Moore’s law predictions. To overcome this problem, approximate computing has recently emerged as a promising solution. Approximate computing is based on the observation that many modern applications are amenable to an approximate, rather than the exact output. Unlike traditional computing, approximate computing tolerates lower accuracy to achieve lower latency by computing over a partial subset instead of the entire input data. Unfortunately, the advancements in approximate computing are primarily geared towards batch analytics and cannot provide low-latency guarantees in the context of stream processing, where new data continuously arrives as an unbounded stream. In this thesis, we design and implement approximate computing techniques for processing and interacting with high-speed and large-scale stream data to achieve low latency and efficient utilization of resources. To achieve these goals, we have designed and built the following approximate data analytics systems: • StreamApprox—a data stream analytics system for approximate computing. This system supports approximate computing for low-latency stream analytics in a transparent way and has an ability to adapt to rapid fluctuations of input data streams. In this system, we designed an online adaptive stratified reservoir sampling algorithm to produce approximate output with bounded error. • IncApprox—a data analytics system for incremental approximate computing. This system adopts approximate and incremental computing in stream processing to achieve high-throughput and low-latency with efficient resource utilization. In this system, we designed an online stratified sampling algorithm that uses self-adjusting computation to produce an incrementally updated approximate output with bounded error. • PrivApprox—a data stream analytics system for privacy-preserving and approximate computing. This system supports high utility and low-latency data analytics and preserves user’s privacy at the same time. The system is based on the combination of privacy-preserving data analytics and approximate computing. • ApproxJoin—an approximate distributed joins system. This system improves the performance of joins — critical but expensive operations in big data systems. In this system, we employed a sketching technique (Bloom filter) to avoid shuffling non-joinable data items through the network as well as proposed a novel sampling mechanism that executes during the join to obtain an unbiased representative sample of the join output. Our evaluation based on micro-benchmarks and real world case studies shows that these systems can achieve significant performance speedup compared to state-of-the-art systems by tolerating negligible accuracy loss of the analytics output. In addition, our systems allow users to systematically make a trade-off between accuracy and throughput/latency and require no/minor modifications to the existing applications