Membership Inference Risks in Quantized Models: A Theoretical and Empirical Study

Quantizing machine learning models has demonstrated its effectiveness in lowering memory and inference costs while maintaining performance levels comparable to those of the original models. In this work, we investigate the impact of quantization procedures on privacy in data-driven models, focusing on their vulnerability to membership inference attacks. Membership Inference Security (MIS) has recently been proposed to characterize the privacy of machine learning models against the most powerful (and possibly unknown) attacks. However, quantifying MIS appears to be computationally very difficult. In this paper, we propose a new MIS indicator for post-training quantization procedures of machine learning models that minimizes an empirical loss. This new indicator is a byproduct of a theoretical asymptotic analysis of the MIS in this context. We also present a methodology for empirically estimating our MIS indicator. Using synthetic datasets and real-world data (in the context of drug discovery), we demonstrate the effectiveness of our approach in assessing and ranking the MIS of different quantizers.