MVG Mechanism: Differential Privacy under Matrix-Valued Query

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.Comment: Appeared in CCS'1

SoK: Chasing Accuracy and Privacy, and Catching Both in Differentially Private Histogram Publication

Histograms and synthetic data are of key importance in data analysis. However, researchers have shown that even aggregated data such as histograms, containing no obvious sensitive attributes, can result in privacy leakage. To enable data analysis, a strong notion of privacy is required to avoid risking unintended privacy violations.Such a strong notion of privacy is differential privacy, a statistical notion of privacy that makes privacy leakage quantifiable. The caveat regarding differential privacy is that while it has strong guarantees for privacy, privacy comes at a cost of accuracy. Despite this trade-off being a central and important issue in the adoption of differential privacy, there exists a gap in the literature regarding providing an understanding of the trade-off and how to address it appropriately. Through a systematic literature review (SLR), we investigate the state-of-the-art within accuracy improving differentially private algorithms for histogram and synthetic data publishing. Our contribution is two-fold: 1) we identify trends and connections in the contributions to the field of differential privacy for histograms and synthetic data and 2) we provide an understanding of the privacy/accuracy trade-off challenge by crystallizing different dimensions to accuracy improvement. Accordingly, we position and visualize the ideas in relation to each other and external work, and deconstruct each algorithm to examine the building blocks separately with the aim of pinpointing which dimension of accuracy improvement each technique/approach is targeting. Hence, this systematization of knowledge (SoK) provides an understanding of in which dimensions and how accuracy improvement can be pursued without sacrificing privacy

Differential Privacy - A Balancing Act

Data privacy is an ever important aspect of data analyses. Historically, a plethora of privacy techniques have been introduced to protect data, but few have stood the test of time. From investigating the overlap between big data research, and security and privacy research, I have found that differential privacy presents itself as a promising defender of data privacy.Differential privacy is a rigorous, mathematical notion of privacy. Nevertheless, privacy comes at a cost. In order to achieve differential privacy, we need to introduce some form of inaccuracy (i.e. error) to our analyses. Hence, practitioners need to engage in a balancing act between accuracy and privacy when adopting differential privacy. As a consequence, understanding this accuracy/privacy trade-off is vital to being able to use differential privacy in real data analyses.In this thesis, I aim to bridge the gap between differential privacy in theory, and differential privacy in practice. Most notably, I aim to convey a better understanding of the accuracy/privacy trade-off, by 1) implementing tools to tweak accuracy/privacy in a real use case, 2) presenting a methodology for empirically predicting error, and 3) systematizing and analyzing known accuracy improvement techniques for differentially private algorithms. Additionally, I also put differential privacy into context by investigating how it can be applied in the automotive domain. Using the automotive domain as an example, I introduce the main challenges that constitutes the balancing act, and provide advice for moving forward

Local Distribution Obfuscation via Probability Coupling

We introduce a general model for the local obfuscation of probability distributions by probabilistic perturbation, e.g., by adding differentially private noise, and investigate its theoretical properties. Specifically, we relax a notion of distribution privacy (DistP) by generalizing it to divergence, and propose local obfuscation mechanisms that provide divergence distribution privacy. To provide f-divergence distribution privacy, we prove that probabilistic perturbation noise should be added proportionally to the Earth mover's distance between the probability distributions that we want to make indistinguishable. Furthermore, we introduce a local obfuscation mechanism, which we call a coupling mechanism, that provides divergence distribution privacy while optimizing the utility of obfuscated data by using exact/approximate auxiliary information on the input distributions we want to protect.Comment: Full version of Allerton 2019 paper (This paper extends some part of the unpublished v3 of arXiv:1812.00939, while v4 of arXiv:1812.00939 extends the other part and is published in ESORICS'19.

Graph Analysis in Decentralized Online Social Networks with Fine-Grained Privacy Protection

Graph analysts cannot directly obtain the global structure in decentralized social networks, and analyzing such a network requires collecting local views of the social graph from individual users. Since the edges between users may reveal sensitive social interactions in the local view, applying differential privacy in the data collection process is often desirable, which provides strong and rigorous privacy guarantees. In practical decentralized social graphs, different edges have different privacy requirements due to the distinct sensitivity levels. However, the existing differentially private analysis of social graphs provide the same protection for all edges. To address this issue, this work proposes a fine-grained privacy notion as well as novel algorithms for private graph analysis. We first design a fine-grained relationship differential privacy (FGR-DP) notion for social graph analysis, which enforces different protections for the edges with distinct privacy requirements. Then, we design algorithms for triangle counting and k-stars counting, respectively, which can accurately estimate subgraph counts given fine-grained protection for social edges. We also analyze upper bounds on the estimation error, including k-stars and triangle counts, and show their superior performance compared with the state-of-the-arts. Finally, we perform extensive experiments on two real social graph datasets and demonstrate that the proposed mechanisms satisfying FGR-DP have better utility than the state-of-the-art mechanisms due to the finer-grained protection