18,535 research outputs found

    Differentially Private Multivariate Statistics with an Application to Contingency Table Analysis

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    Differential privacy (DP) has become a rigorous central concept in privacy protection for the past decade. Among various notions of DP, ff-DP is an easily interpretable and informative concept that tightly captures privacy level by comparing trade-off functions obtained from the hypothetical test of how well the mechanism recognizes individual information in the dataset. We adopt the Gaussian differential privacy (GDP), a canonical parametric family of ff-DP. The Gaussian mechanism is a natural and fundamental mechanism that tightly achieves GDP. However, the ordinary multivariate Gaussian mechanism is not optimal with respect to statistical utility. To improve the utility, we develop the rank-deficient and James-Stein Gaussian mechanisms for releasing private multivariate statistics based on the geometry of multivariate Gaussian distribution. We show that our proposals satisfy GDP and dominate the ordinary Gaussian mechanism with respect to L2L_2-cost. We also show that the Laplace mechanism, a prime mechanism in ε\varepsilon-DP framework, is sub-optimal than Gaussian-type mechanisms under the framework of GDP. For a fair comparison, we calibrate the Laplace mechanism to the global sensitivity of the statistic with the exact approach to the trade-off function. We also develop the optimal parameter for the Laplace mechanism when applied to contingency tables. Indeed, we show that the Gaussian-type mechanisms dominate the Laplace mechanism in contingency table analysis. In addition, we apply our findings to propose differentially private χ2\chi^2-tests on contingency tables. Numerical results demonstrate that differentially private parametric bootstrap tests control the type I error rates and show higher power than other natural competitors

    The fundamental limits of statistical data privacy

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    The Internet is shaping our daily lives. On the one hand, social networks like Facebook and Twitter allow people to share their precious moments and opinions with virtually anyone around the world. On the other, services like Google, Netflix, and Amazon allow people to look up information, watch movies, and shop online anytime, anywhere. However, with this unprecedented level of connectivity comes the danger of being monitored. There is an increasing tension between the need to share data and the need to preserve the privacy of Internet users. The need for privacy appears in three main contexts: (1) the global privacy context, as in when private companies and public institutions release personal information about individuals to the public; (2) the local privacy context, as in when individuals disclose their personal information with potentially malicious service providers; (3) the multi-party privacy context, as in when different parties cooperate to interactively compute a function that is defined over all the parties' data. Differential privacy has recently surfaced as a strong measure of privacy in all three contexts. Under differential privacy, privacy is achieved by randomizing the data before releasing it. This leads to a fundamental tradeoff between privacy and utility. In this thesis, we take a concrete step towards understanding the fundamental structure of privacy mechanisms that achieve the best privacy-utility tradeoff. This tradeoff is formulated as a constrained optimization problem: maximize utility subject to differential privacy constraints. We show, perhaps surprisingly, that in all three privacy contexts, the optimal privacy mechanisms have the same combinatorial staircase structure. This deep result is a direct consequence of the geometry of the constraints imposed by differential privacy on the privatization mechanisms

    On the Measurement of Privacy as an Attacker's Estimation Error

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    A wide variety of privacy metrics have been proposed in the literature to evaluate the level of protection offered by privacy enhancing-technologies. Most of these metrics are specific to concrete systems and adversarial models, and are difficult to generalize or translate to other contexts. Furthermore, a better understanding of the relationships between the different privacy metrics is needed to enable more grounded and systematic approach to measuring privacy, as well as to assist systems designers in selecting the most appropriate metric for a given application. In this work we propose a theoretical framework for privacy-preserving systems, endowed with a general definition of privacy in terms of the estimation error incurred by an attacker who aims to disclose the private information that the system is designed to conceal. We show that our framework permits interpreting and comparing a number of well-known metrics under a common perspective. The arguments behind these interpretations are based on fundamental results related to the theories of information, probability and Bayes decision.Comment: This paper has 18 pages and 17 figure

    Efficient Private ERM for Smooth Objectives

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    In this paper, we consider efficient differentially private empirical risk minimization from the viewpoint of optimization algorithms. For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not only achieves nearly optimal utility, but also significantly improves the running time of previous state-of-the-art private optimization algorithms, for both ϵ\epsilon-DP and (ϵ,δ)(\epsilon, \delta)-DP. For non-convex but smooth objectives, we propose an RRPSGD (Random Round Private Stochastic Gradient Descent) algorithm, which provably converges to a stationary point with privacy guarantee. Besides the expected utility bounds, we also provide guarantees in high probability form. Experiments demonstrate that our algorithm consistently outperforms existing method in both utility and running time

    Privacy-Compatibility For General Utility Metrics

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    In this note, we present a complete characterization of the utility metrics that allow for non-trivial differential privacy guarantees
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