Sparse Vector Technique Research Articles

Confidence Intervals for Private Query Processing

Whenever randomness is involved in query processing, confidence intervals are commonly returned to the user to indicate the statistical significance of the query answer. However, this problem has not been explicitly addressed under differential privacy, which must use randomness by definition. For some classical mechanisms whose noise distribution does not depend on the input, such as the Laplace and the Gaussian mechanism, deriving confidence intervals is easy. But the problem becomes nontrivial for queries whose global sensitivity is large or unbounded, for which these classical mechanisms cannot be applied. There are three main techniques in the literature for dealing with such queries: the exponential mechanism, the sparse vector technique, and the smooth sensitivity. In this paper, for each of the three techniques we design mechanisms to produce confidence intervals that are (1) differentially private; (2) correct, i.e., the interval contains the true query answer with the specified confidence level; and (3) have a utility guarantee matching that of the original mechanism, up to constant factors. Then we show how to apply our techniques to a variety of problems ranging from simple statistics (e.g., mean, median, maximum) to graph pattern counting and conjunctive queries.

Privately vertically mining of sequential patterns based on differential privacy with high efficiency and utility

Sequential pattern mining is one of the fundamental tools for many important data analysis tasks, such as web browsing behavior analysis. Based on frequent patterns, decision-makers can obtain both economic gains and social values. Sequential data, on the other hand, frequently contain sensitive information, and directly analyzing these data will raise user concerns from a privacy perspective. Differential privacy (DP), as the most popular privacy model, has been employed to address this privacy concern. Most existing DP-Solutions are designed to combine horizontal sequence pattern mining algorithms with differential privacy. Due to the inefficiency of horizontal algorithms, their DP-Solutions cannot ensure high efficiency and accuracy while offering a high privacy guarantee. Therefore, we proposed privVertical, a new private sequence pattern mining scheme combining the vertical mining algorithm with differential privacy to achieve the above objective. Unlike DP-solutions based on horizontal algorithms, privVertical can promote efficiency by avoiding performing costly database scans or costly projection database constructions. Moreover, to promote accuracy, a differentially private hash MapList (called privHashMap) is designed to record frequent concurrency items and their noisy support based on the Sparse Vector Technique. PrivHashMap is used to pre-pruning excessive infrequent candidate sequences in private mining, and Sparse Vector Technique is used to promote the accuracy of PrivHashMap. After pruning these invalid candidate sequences, less noise is required to achieve the same level of privacy, increasing the accuracy of private mining. Theoretical privacy analysis proves privVertical satisfies varepsilon-differential privacy. Experiments show that privVertical achieves higher accuracy and efficiency while achieving the same privacy level.

Boosting Accuracy of Differentially Private Federated Learning in Industrial IoT With Sparse Responses

Empowered by 5G, it has been extensively explored by existing works on the deployment of differentially private federated learning (DPFL) in the Industrial Internet of Things (IIoT). Through federated learning, decentralized IIoT devices can collaboratively train a machine learning model by merely exchanging model gradients with a parameter server (PS) for multiple global iterations. Differentially private (DP) mechanisms will be incorporated by IIoT devices (also called clients) to prevent the leakage of privacy due to the exposure of gradients because original gradients will be distorted DP noises. Yet, learning with distorted gradients can seriously deteriorate model accuracy, making DPFL unusable in reality. To address this problem, we propose a novel DPFL with sparse responses (DPFL-SR) algorithm, which applies the sparse vector technique to reduce the privacy budget consumption in each global iteration. Specifically, DPFL-SR evaluates the value of each gradient, and only distorts and uploads significant gradients to the PS because significant gradients are more essential for model training. Since insignificant gradients are not disclosed, the reserved privacy budget can be used to return significant gradients for more iterations so that DPFL-SR can achieve higher model accuracy without lowering the privacy protection level. Extensive experiments are conducted with the MNIST and Fashion-MNIST datasets to demonstrate the practicability and superiority of DPFL-SR in IIoT systems.

Privacy accounting εconomics: Improving differential privacy composition via a posteriori bounds

Differential privacy (DP) is a widely used notion for reasoning about privacy when publishing aggregate data. In this paper, we observe that certain DP mechanisms are amenable to a posteriori privacy analysis that exploits the fact that some outputs leak less information about the input database than others. To exploit this phenomenon, we introduce output differential privacy (ODP) and a new composition experiment, and leverage these new constructs to obtain significant privacy budget savings and improved privacy–utility tradeoffs under composition. All of this comes at no cost in terms of privacy; we do not weaken the privacy guarantee. To demonstrate the applicability of our a posteriori privacy analysis techniques, we analyze two well-known mechanisms: the Sparse Vector Technique and the Propose-Test-Release framework. We then show how our techniques can be used to save privacy budget in more general contexts: when a differentially private iterative mechanism terminates before its maximal number of iterations is reached, and when the output of a DP mechanism provides unsatisfactory utility. Examples of the former include iterative optimization algorithms, whereas examples of the latter include training a machine learning model with a large generalization error. Our techniques can be applied beyond the current paper to refine the analysis of existing DP mechanisms or guide the design of future mechanisms.

ABCDP: Approximate Bayesian Computation with Differential Privacy.

We developed a novel approximate Bayesian computation (ABC) framework, ABCDP, which produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the sparse vector technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a condition (whether a quantity of interest is above/below a threshold) is met. If the condition is sparsely met during the repeated queries, SVT can drastically reduce the cumulative privacy loss, unlike the usual case where every query incurs the privacy loss. In ABC, the quantity of interest is the distance between observed and simulated data, and only when the distance is below a threshold can we take the corresponding prior sample as a posterior sample. Hence, applying SVT to ABC is an organic way to transform an ABC algorithm to a privacy-preserving variant with minimal modification, but yields the posterior samples with a high privacy level. We theoretically analyzed the interplay between the noise added for privacy and the accuracy of the posterior samples. We apply ABCDP to several data simulators and show the efficacy of the proposed framework.

Differentially Private Event-Triggered Sampling

This paper describes a differentially private event-triggered sampling mechanism to select measurement samples from a data sequence whose dynamics can be modelled by a stochastic linear system. The mechanism produces subsequences that can be used to reestimate the original sequence relatively accurately and the differential privacy constraint guarantees that these subsequences are insensitive to certain variations in the input sequence. The subsampling process can be motivated by the presence of communication bandwidth constraints, but also provides an additional tool to explore achievable privacy-utility tradeoffs in privacy-preserving signal processing and control. Event-triggered sampling can offer benefits over periodic subsampling by attempting to select the most useful samples, but the fact that it leaks information when no sampling occurs must be carefully taken into account to meet the differential privacy requirement. We propose a design using a stochastic sampling threshold, leveraging the "sparse vector technique" from differential privacy to incur a privacy loss only when samples are actually released. This design includes a suboptimal but tractable recursive finite-dimensional estimator that can also be used to re-estimate the original sequence from the differentially private noisy subsequence.

Understanding the sparse vector technique for differential privacy

The Sparse Vector Technique (SVT) is a fundamental technique for satisfying differential privacy and has the unique quality that one can output some query answers without apparently paying any privacy cost. SVT has been used in both the interactive setting, where one tries to answer a sequence of queries that are not known ahead of the time, and in the non-interactive setting, where all queries are known. Because of the potential savings on privacy budget, many variants for SVT have been proposed and employed in privacy-preserving data mining and publishing. However, most variants of SVT are actually not private. In this paper, we analyze these errors and identify the misunderstandings that likely contribute to them. We also propose a new version of SVT that provides better utility, and introduce an effective technique to improve the performance of SVT. These enhancements can be applied to improve utility in the interactive setting. Through both analytical and experimental comparisons, we show that, in the non-interactive setting (but not the interactive setting), the SVT technique is unnecessary, as it can be replaced by the Exponential Mechanism (EM) with better accuracy.

Differential Privacy: From Theory to Practice

Over the last decade, differential privacy (DP) has emerged as the de facto standard privacy notion for research in privacy-preserving data analysis and publishing. The DP notion offers strong privacy guarantee and has been applied to many data analysis tasks. This Synthesis Lecture is the first of two volumes on differential privacy. This lecture differs from the existing books and surveys on differential privacy in that we take an approach balancing theory and practice. We focus on empirical accuracy performances of algorithms rather than asymptotic accuracy guarantees. At the same time, we try to explain why these algorithms have those empirical accuracy performances. We also take a balanced approach regarding the semantic meanings of differential privacy, explaining both its strong guarantees and its limitations. We start by inspecting the definition and basic properties of DP, and the main primitives for achieving DP. Then, we give a detailed discussion on the the semantic privacy guarantee provided by DP and the caveats when applying DP. Next, we review the state of the art mechanisms for publishing histograms for low-dimensional datasets, mechanisms for conducting machine learning tasks such as classification, regression, and clustering, and mechanisms for publishing information to answer marginal queries for high-dimensional datasets. Finally, we explain the sparse vector technique, including the many errors that have been made in the literature using it. The planned Volume 2 will cover usage of DP in other settings, including high-dimensional datasets, graph datasets, local setting, location privacy, and so on. We will also discuss various relaxations of DP.

DPcode: Privacy-Preserving Frequent Visual Patterns Publication on Cloud

Nowadays, cloud has become a promising multimedia data processing and sharing platform. Many institutes and companies plan to outsource and share their large-scale video and image datasets on cloud for scientific research and public interest. Among various video applications, the discovery of frequent visual patterns over graphical data is an exploratory and important technique. However, the privacy concerns over the leakage of sensitive information contained in the videos/images impedes the further implementation. Although the frequent visual patterns mining (FVPM) algorithm aggregates summary over individual frames and seems not to pose privacy threat, the private information contained in individual frames still may be leaked from the statistical result. In this paper, we study the problem of privacy-preserving publishing of graphical data FVPM on cloud. We propose the first differentially private frequent visual patterns mining algorithm for graphical data, named DPcode. We propose a novel mechanism that integrates the privacy-preserving visual word conversion with the differentially private mechanism under the noise allocation strategy of the sparse vector technique. The optimized algorithms properly allocate the privacy budgets among different phases in FPM algorithm over images and reduce the corresponding data distortion. Extensive experiments are conducted based on datasets commonly used in visual mining algorithms. The results show that our approach achieves high utility while satisfying a practical privacy requirement.

Choosing the appropriate boundary for adaptive reduction (power system load flow)

Adaptive reduction method provides a way to retain the maximum sparsity in the power network matrix after reduction. It also provides a fast reduction calculation using the sparse vector technique, making it attractive for online load flow analysis applications. The question of determining the minimal reduced model size to work in conjunction with adaptive reduction is considered. Guidelines are developed for choosing the appropriate boundary when this can be done offline. A method is then presented for determining the boundary online, and its advantages are discussed. By choosing the appropriate boundary for adaptive reduction, the best size and sparsity of the reduced network model can be obtained to get the best solution speed. >