Local FDR Membership Inference Attacks: Multiple Testing and the Role of Ridge Regularization

Membership inference attacks (MIAs) are commonly formulated as single-sample hypothesis tests with false positive rate control. However, realistic adversaries often test many candidate samples and aggregate the declared members, making membership inference a multiple testing problem. In this regime, per-sample calibration can produce unreliable sets of inferred members. We develop a false discovery rate (FDR)-controlled framework for membership inference based on the classical local FDR formulation. We instantiate the framework for high dimensional ridge regression. Under a conditional sufficiency condition, we establish FDR guarantee of the proposed method, and derive an asymptotic characterization of its detection power in high-dimensional regimes under an isotropic Gaussian design. Our analysis shows that, under FDR control, stronger ridge regularization reduces membership inference risk. Experiments on synthetic and a real-world dataset validate the theoretical findings and demonstrate that the proposed methods provide more reliable membership discoveries than existing attacks.