Impact of Prior Knowledge and Data Correlation on Privacy Leakage: A Unified Analysis

by   Yanan Li, et al.

It has been widely understood that differential privacy (DP) can guarantee rigorous privacy against adversaries with arbitrary prior knowledge. However, recent studies demonstrate that this may not be true for correlated data, and indicate that three factors could influence privacy leakage: the data correlation pattern, prior knowledge of adversaries, and sensitivity of the query function. This poses a fundamental problem: what is the mathematical relationship between the three factors and privacy leakage? In this paper, we present a unified analysis of this problem. A new privacy definition, named prior differential privacy (PDP), is proposed to evaluate privacy leakage considering the exact prior knowledge possessed by the adversary. We use two models, the weighted hierarchical graph (WHG) and the multivariate Gaussian model to analyze discrete and continuous data, respectively. We demonstrate that positive, negative, and hybrid correlations have distinct impacts on privacy leakage. Considering general correlations, a closed-form expression of privacy leakage is derived for continuous data, and a chain rule is presented for discrete data. Our results are valid for general linear queries, including count, sum, mean, and histogram. Numerical experiments are presented to verify our theoretical analysis.


page 4

page 5

page 6

page 8

page 9

page 10

page 13

page 14


Quantifying Differential Privacy in Continuous Data Release under Temporal Correlations

Differential Privacy (DP) has received increasing attention as a rigorou...

Correlated Data in Differential Privacy: Definition and Analysis

Differential privacy is a rigorous mathematical framework for evaluating...

(α,β)-Leakage: A Unified Privacy Leakage Measure

We introduce a family of information leakage measures called maximal (α,...

On the Choice of Databases in Differential Privacy Composition

Differential privacy (DP) is a widely applied paradigm for releasing dat...

Explaining epsilon in differential privacy through the lens of information theory

The study of leakage measures for privacy has been a subject of intensiv...

Preserving Both Privacy and Utility in Network Trace Anonymization

As network security monitoring grows more sophisticated, there is an inc...

Generalization Bounds for Stochastic Gradient Langevin Dynamics: A Unified View via Information Leakage Analysis

Recently, generalization bounds of the non-convex empirical risk minimiz...

Please sign up or login with your details

Forgot password? Click here to reset