Why Does Differential Privacy with Large Epsilon Defend Against Practical Membership Inference Attacks?
This work addresses the problem of justifying differential privacy deployments with large parameters for practitioners, offering a more realistic privacy notion that bridges theory and empirical observations.
The paper tackles the gap between differential privacy theory and practice by explaining why large privacy parameters (e.g., ε ≥ 7) defend against practical membership inference attacks, despite weak theoretical guarantees. It introduces practical membership privacy (PMP) to model attacker uncertainty and shows that large DP parameters often yield strong PMP guarantees, providing principled guidance for parameter selection.
For small privacy parameter $ε$, $ε$-differential privacy (DP) provides a strong worst-case guarantee that no membership inference attack (MIA) can succeed at determining whether a person's data was used to train a machine learning model. The guarantee of DP is worst-case because: a) it holds even if the attacker already knows the records of all but one person in the data set; and b) it holds uniformly over all data sets. In practical applications, such a worst-case guarantee may be overkill: practical attackers may lack exact knowledge of (nearly all of) the private data, and our data set might be easier to defend, in some sense, than the worst-case data set. Such considerations have motivated the industrial deployment of DP models with large privacy parameter (e.g. $ε\geq 7$), and it has been observed empirically that DP with large $ε$ can successfully defend against state-of-the-art MIAs. Existing DP theory cannot explain these empirical findings: e.g., the theoretical privacy guarantees of $ε\geq 7$ are essentially vacuous. In this paper, we aim to close this gap between theory and practice and understand why a large DP parameter can prevent practical MIAs. To tackle this problem, we propose a new privacy notion called practical membership privacy (PMP). PMP models a practical attacker's uncertainty about the contents of the private data. The PMP parameter has a natural interpretation in terms of the success rate of a practical MIA on a given data set. We quantitatively analyze the PMP parameter of two fundamental DP mechanisms: the exponential mechanism and Gaussian mechanism. Our analysis reveals that a large DP parameter often translates into a much smaller PMP parameter, which guarantees strong privacy against practical MIAs. Using our findings, we offer principled guidance for practitioners in choosing the DP parameter.