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 $(ε,δ)$-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.
Make Up Your Mind: The Price of Online Queries in Differential Privacy
Harvard University John A. Paulson School of Engineering and Applied Sciences（哈佛大学约翰·A·保尔森工程与应用科学学院）；Yale University（耶鲁大学）；Northeastern University College of Computer and Information Science（东北大学计算机与信息科学学院）
Shanghai Jiao Tong University（上海交通大学）；Southern University of Science and Technology（南方科技大学）；Huawei International（华为国际）；John Hopcroft Center（约翰·霍普克罗夫特中心）；AI Institute, Shanghai Jiao Tong University（上海交通大学人工智能研究院）
A Unified Framework for Generic, Query-Focused, Privacy Preserving and Update Summarization using Submodular Information Measures
Department of Computer Science, Indian Institute of Technology Bombay（印度理工学院孟买分校计算机科学系）；Department of Computer Science, University of Texas at Dallas（得克萨斯大学达拉斯分校计算机科学系）；Department of Electrical and Computer Engineering, University of Washington, Seattle（华盛顿大学西雅图分校电气与计算机工程系）；School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai（塔塔基础研究所孟买技术与计算机科学学院）
Convex Optimization for Linear Query Processing under Approximate Differential Privacy
South China University of Technology（华南理工大学）；Hamad Bin Khalifa University（哈马德·本·哈利法大学）；Illinois at Singapore Pte. Ltd（伊利诺伊大学新加坡私人有限公司）；Foshan University（佛山科学技术学院）
