Parameters or Privacy: A Provable Tradeoff Between Overparameterization and Membership Inference
This reveals a hidden privacy cost for practitioners using overparameterized models, which is incremental as it builds on prior empirical findings.
The paper tackles the problem of overparameterized models being more vulnerable to membership inference attacks, proving theoretically for linear regression that vulnerability increases with parameter count and showing empirically that this extends to nonlinear models.
A surprising phenomenon in modern machine learning is the ability of a highly overparameterized model to generalize well (small error on the test data) even when it is trained to memorize the training data (zero error on the training data). This has led to an arms race towards increasingly overparameterized models (c.f., deep learning). In this paper, we study an underexplored hidden cost of overparameterization: the fact that overparameterized models may be more vulnerable to privacy attacks, in particular the membership inference attack that predicts the (potentially sensitive) examples used to train a model. We significantly extend the relatively few empirical results on this problem by theoretically proving for an overparameterized linear regression model in the Gaussian data setting that membership inference vulnerability increases with the number of parameters. Moreover, a range of empirical studies indicates that more complex, nonlinear models exhibit the same behavior. Finally, we extend our analysis towards ridge-regularized linear regression and show in the Gaussian data setting that increased regularization also increases membership inference vulnerability in the overparameterized regime.