Uncertainty, Calibration, and Membership Inference Attacks: An Information-Theoretic Perspective

In a membership inference attack (MIA), an attacker exploits the overconfidence exhibited by typical machine learning models to determine whether a specific data point was used to train a target model. In this paper, we analyze the performance of the state-of-the-art likelihood ratio attack (LiRA) within an information-theoretical framework that allows the investigation of the impact of the aleatoric uncertainty in the true data generation process, of the epistemic uncertainty caused by a limited training data set, and of the calibration level of the target model. We compare three different settings, in which the attacker receives decreasingly informative feedback from the target model: confidence vector (CV) disclosure, in which the output probability vector is released; true label confidence (TLC) disclosure, in which only the probability assigned to the true label is made available by the model; and decision set (DS) disclosure, in which an adaptive prediction set is produced as in conformal prediction. We derive bounds on the advantage of an MIA adversary with the aim of offering insights into the impact of uncertainty and calibration on the effectiveness of MIAs. Simulation results demonstrate that the derived analytical bounds predict well the effectiveness of MIAs. The work of M. Zhu, C. Guo and C. Feng was supported by the National Natural Science Foundation of China (62371070), by the Fundamental Research Funds for the Central Universities (2021XD-A01-1), and by the Beijing Natural Science Foundation (L222043).