Modelling and Quantifying Membership Information Leakage in Machine Learning

TL;DR

This paper models and quantifies how much membership information about training data can be leaked from machine learning models, using information theory, and explores factors affecting leakage and privacy-preserving techniques.

Contribution

It introduces a mutual information-based measure of membership leakage, derives bounds, and analyzes how model complexity, dataset size, and regularization influence leakage.

Findings

Leakage decreases with larger training datasets and higher regularization.

Complex models like deep neural networks leak more membership information.

Adding Gaussian differential privacy noise reduces leakage significantly.

Abstract

Machine learning models have been shown to be vulnerable to membership inference attacks, i.e., inferring whether individuals' data have been used for training models. The lack of understanding about factors contributing success of these attacks motivates the need for modelling membership information leakage using information theory and for investigating properties of machine learning models and training algorithms that can reduce membership information leakage. We use conditional mutual information leakage to measure the amount of information leakage from the trained machine learning model about the presence of an individual in the training dataset. We devise an upper bound for this measure of information leakage using Kullback--Leibler divergence that is more amenable to numerical computation. We prove a direct relationship between the Kullback--Leibler membership information leakage and the probability of success for a hypothesis-testing adversary examining whether a particular data record belongs to the training dataset of a machine learning model. We show that the mutual information leakage is a decreasing function of the training dataset size and the regularization weight. We also prove that, if the sensitivity of the machine learning model (defined in terms of the derivatives of the fitness with respect to model parameters) is high, more membership information is potentially leaked. This illustrates that complex models, such as deep neural networks, are more susceptible to membership inference attacks in comparison to simpler models with fewer degrees of freedom. We show that the amount of the membership information leakage is reduced by $\mathcal{O}(\log^{1/2}(\delta^{-1})\epsilon^{-1})$ when using Gaussian $(\epsilon,\delta)$-differentially-private additive noises.