Local differential privacy (LDP) can provide each user with strong privacy guarantees under untrusted data curators while ensuring accurate statistics derived from privatized data. Due to its powerfulness, LDP has been widely adopted to protect privacy in various tasks (e.g., heavy hitters discovery, probability estimation) and systems (e.g., Google Chrome, Apple iOS). Although @math -LDP has been proposed for many years, the more general notion of @math -LDP has only been studied in very few papers, which mainly consider mean estimation for numeric data. Besides, prior solutions achieve @math -LDP by leveraging Gaussian mechanism, which leads to low accuracy of the aggregated results. In this paper, we propose novel mechanisms that achieve @math -LDP with high utility in data analytics and machine learning. Specifically, we first design @math -LDP algorithms for collecting multi-dimensional numeric data, which can ensure higher accuracy than the optimal Gaussian mechanism while guaranteeing strong privacy for each user. Then, we investigate different local protocols for categorical attributes under @math -LDP. Furthermore, we conduct theoretical analysis on the error bound and variance of the proposed algorithms. Experimental results on real and synthetic datasets demonstrate the high data utility of our proposed algorithms on both simple data statistics and complex machine learning models.
Local differential privacy (LDP) is a recently proposed privacy standard for collecting and analyzing data, which has been used, e.g., in the Chrome browser, iOS and macOS. In LDP, each user perturbs her information locally, and only sends the randomized version to an aggregator who performs analyses, which protects both the users and the aggregator against private information leaks. Although LDP has attracted much research attention in recent years, the majority of existing work focuses on applying LDP to complex data and or analysis tasks. In this paper, we point out that the fundamental problem of collecting multidimensional data under LDP has not been addressed sufficiently, and there remains much room for improvement even for basic tasks such as computing the mean value over a single numeric attribute under LDP. Motivated by this, we first propose novel LDP mechanisms for collecting a numeric attribute, whose accuracy is at least no worse (and usually better) than existing solutions in terms of worst-case noise variance. Then, we extend these mechanisms to multidimensional data that can contain both numeric and categorical attributes, where our mechanisms always outperform existing solutions regarding worst-case noise variance. As a case study, we apply our solutions to build an LDP-compliant stochastic gradient descent algorithm (SGD), which powers many important machine learning tasks. Experiments using real datasets confirm the effectiveness of our methods, and their advantages over existing solutions. Organizations with a large user base, such as Samsung and Google, can potentially benefit from collecting and mining users' data. However, doing so raises privacy concerns, and risks accidental privacy breaches with serious consequences. Local differential privacy (LDP) techniques address this problem by only collecting randomized answers from each user, with guarantees of plausible deniability; meanwhile, the aggregator can still build accurate models and predictors by analyzing large amounts of such randomized data. So far, existing LDP solutions either have severely restricted functionality, or focus mainly on theoretical aspects such as asymptotical bounds rather than practical usability and performance. Motivated by this, we propose Harmony, a practical, accurate and efficient system for collecting and analyzing data from smart device users, while satisfying LDP. Harmony applies to multi-dimensional data containing both numerical and categorical attributes, and supports both basic statistics (e.g., mean and frequency estimates), and complex machine learning tasks (e.g., linear regression, logistic regression and SVM classification). Experiments using real data confirm Harmony's effectiveness. Working under a model of privacy in which data remain private even from the statistician, we study the tradeoff between privacy guarantees and the risk of the resulting statistical estimators. We develop private versions of classical information-theoretical bounds, in particular those due to Le Cam, Fano, and Assouad. These inequalities allow for a precise characterization of statistical rates under local privacy constraints and the development of provably (minimax) optimal estimation procedures. We provide a treatment of several canonical families of problems: mean estimation and median estimation, generalized linear models, and nonparametric density estimation. For all of these families, we provide lower and upper bounds that match up to constant factors, and exhibit new (optimal) privacy-preserving mechanisms and computationally efficient estimators that achieve the bounds. Additionally, we present a variety of experimental results for estimation problems involving sensitive data, including salaries, censored blog posts and articles, and drug abuse; these experiments demonstrate the importance of deriving optimal procedures. Supplementary materials for this article are available online.