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Register a new userA Differential Privacy Mechanism Design Under Matrix-Valued Query
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Added by
Thee Chanyaswad
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Traditionally, differential privacy mechanism design has 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 sub-optimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. In this work, we consider the design of differential privacy mechanism specifically for a matrix-valued query function. The proposed solution is to utilize a matrix-variate noise, as opposed to the traditional scalar-valued noise. Particularly, 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. We prove that the MVG mechanism preserves $(epsilon,delta)$-differential privacy, and show that it allows the structural characteristics of the matrix-valued query function to naturally be exploited. Furthermore, due to the multi-dimensional nature of the MVG mechanism and the matrix-valued query, we introduce the concept of directional noise, which can be utilized to mitigate the impact the noise has on the utility of the query. Finally, we demonstrate the performance of the MVG mechanism and the advantages of directional noise 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. Our work thus presents a promising prospect for both future research and implementation of differential privacy for matrix-valued query functions.
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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.
We propose a new mechanism to accurately answer a user-provided set of linear counting queries under local differential privacy (LDP). Given a set of linear counting queries (the workload) our mechanism automatically adapts to provide accuracy on the workload queries. We define a parametric class of mechanisms that produce unbiased estimates of the workload, and formulate a constrained optimization problem to select a mechanism from this class that minimizes expected total squared error. We solve this optimization problem numerically using projected gradient descent and provide an efficient implementation that scales to large workloads. We demonstrate the effectiveness of our optimization-based approach in a wide variety of settings, showing that it outperforms many competitors, even outperforming existing mechanisms on the workloads for which they were intended.
The wide deployment of machine learning in recent years gives rise to a great demand for large-scale and high-dimensional data, for which the privacy raises serious concern. Differential privacy (DP) mechanisms are conventionally developed for scalar values, not for structural data like matrices. Our work proposes Improved Matrix Gaussian Mechanism (IMGM) for matrix-valued DP, based on the necessary and sufficient condition of $ (varepsilon,delta) $-differential privacy. IMGM only imposes constraints on the singular values of the covariance matrices of the noise, which leaves room for design. Among the legitimate noise distributions for matrix-valued DP, we find the optimal one turns out to be i.i.d. Gaussian noise, and the DP constraint becomes a noise lower bound on each element. We further derive a tight composition method for IMGM. Apart from the theoretical analysis, experiments on a variety of models and datasets also verify that IMGM yields much higher utility than the state-of-the-art mechanisms at the same privacy guarantee.
As massive data are produced from small gadgets, federated learning on mobile devices has become an emerging trend. In the federated setting, Stochastic Gradient Descent (SGD) has been widely used in federated learning for various machine learning models. To prevent privacy leakages from gradients that are calculated on users sensitive data, local differential privacy (LDP) has been considered as a privacy guarantee in federated SGD recently. However, the existing solutions have a dimension dependency problem: the injected noise is substantially proportional to the dimension $d$. In this work, we propose a two-stage framework FedSel for federated SGD under LDP to relieve this problem. Our key idea is that not all dimensions are equally important so that we privately select Top-k dimensions according to their contributions in each iteration of federated SGD. Specifically, we propose three private dimension selection mechanisms and adapt the gradient accumulation technique to stabilize the learning process with noisy updates. We also theoretically analyze privacy, accuracy and time complexity of FedSel, which outperforms the state-of-the-art solutions. Experiments on real-world and synthetic datasets verify the effectiveness and efficiency of our framework.
Traditional differential privacy is independent of the data distribution. However, this is not well-matched with the modern machine learning context, where models are trained on specific data. As a result, achieving meaningful privacy guarantees in ML often excessively reduces accuracy. We propose Bayesian differential privacy (BDP), which takes into account the data distribution to provide more practical privacy guarantees. We also derive a general privacy accounting method under BDP, building upon the well-known moments accountant. Our experiments demonstrate that in-distribution samples in classic machine learning datasets, such as MNIST and CIFAR-10, enjoy significantly stronger privacy guarantees than postulated by DP, while models maintain high classification accuracy.
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