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Added by
Hilal Asi
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We develop two notions of instance optimality in differential privacy, inspired by classical statistical theory: one by defining a local minimax risk and the other by considering unbiased mechanisms and analogizing the Cramer-Rao bound, and we show that the local modulus of continuity of the estimand of interest completely determines these quantities. We also develop a complementary collection mechanisms, which we term the inverse sensitivity mechanisms, which are instance optimal (or nearly instance optimal) for a large class of estimands. Moreover, these mechanisms uniformly outperform the smooth sensitivity framework on each instance for several function classes of interest, including real-valued continuous functions. We carefully present two instantiations of the mechanisms for median and robust regression estimation with corresponding experiments.
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Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. To address this challenge, we propose a novel differential privacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which adds a matrix-valued noise drawn from a matrix-variate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves $(epsilon,delta)$-differential privacy. Furthermore, we introduce the concept of directional noise made possible by the design of the MVG mechanism. Directional noise allows the impact of the noise on the utility of the matrix-valued query function to be moderated. Finally, we experimentally demonstrate the performance of our mechanism using three matrix-valued queries on three privacy-sensitive datasets. We find that the MVG mechanism notably outperforms four previous state-of-the-art approaches, and provides comparable utility to the non-private baseline.
In this rejoinder, we aim to address two broad issues that cover most comments made in the discussion. First, we discuss some theoretical aspects of our work and comment on how this work might impact the theoretical foundation of privacy-preserving data analysis. Taking a practical viewpoint, we next discuss how f-differential privacy (f-DP) and Gaussian differential privacy (GDP) can make a difference in a range of applications.
Membership inference attacks seek to infer the membership of individual training instances of a privately trained model. This paper presents a membership privacy analysis and evaluation system, called MPLens, with three unique contributions. First, through MPLens, we demonstrate how membership inference attack methods can be leveraged in adversarial machine learning. Second, through MPLens, we highlight how the vulnerability of pre-trained models under membership inference attack is not uniform across all classes, particularly when the training data itself is skewed. We show that risk from membership inference attacks is routinely increased when models use skewed training data. Finally, we investigate the effectiveness of differential privacy as a mitigation technique against membership inference attacks. We discuss the trade-offs of implementing such a mitigation strategy with respect to the model complexity, the learning task complexity, the dataset complexity and the privacy parameter settings. Our empirical results reveal that (1) minority groups within skewed datasets display increased risk for membership inference and (2) differential privacy presents many challenging trade-offs as a mitigation technique to membership inference risk.
Location-Based Services (LBSs) provide invaluable aid in the everyday activities of many individuals, however they also pose serious threats to the user privacy. There is, therefore, a growing interest in the development of mechanisms to protect location privacy during the use of LBSs. Nowadays, the most popular methods are probabilistic, and the so-called optimal method achieves an optimal trade-off between privacy and utility by using linear optimization techniques. Unfortunately, due to the complexity of linear programming, the method is unfeasible for a large number n of locations, because the constraints are $O(n^3)$. In this paper, we propose a technique to reduce the number of constraints to $O(n^2)$, at the price of renouncing to perfect optimality. We show however that on practical situations the utility loss is quite acceptable, while the gain in performance is significant.
We address the problem of how to obfuscate texts by removing stylistic clues which can identify authorship, whilst preserving (as much as possible) the content of the text. In this paper we combine ideas from generalised differential privacy and machine learning techniques for text processing to model privacy for text documents. We define a privacy mechanism that operates at the level of text documents represented as bags-of-words - these representations are typical in machine learning and contain sufficient information to carry out many kinds of classification tasks including topic identification and authorship attribution (of the original documents). We show that our mechanism satisfies privacy with respect to a metric for semantic similarity, thereby providing a balance between utility, defined by the semantic content of texts, with the obfuscation of stylistic clues. We demonstrate our implementation on a fan fiction dataset, confirming that it is indeed possible to disguise writing style effectively whilst preserving enough information and variation for accurate content classification tasks.
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