  This paper studies defense mechanisms against model inversion (MI) attacks --
a type of privacy attacks aimed at inferring information about the training
data distribution given the access to a target machine learning model. Existing
defense mechanisms rely on model-specific heuristics or noise injection. While
being able to mitigate attacks, existing methods significantly hinder model
performance. There remains a question of how to design a defense mechanism that
is applicable to a variety of models and achieves better utility-privacy
tradeoff. In this paper, we propose the Mutual Information Regularization based
Defense (MID) against MI attacks. The key idea is to limit the information
about the model input contained in the prediction, thereby limiting the ability
of an adversary to infer the private training attributes from the model
prediction. Our defense principle is model-agnostic and we present tractable
approximations to the regularizer for linear regression, decision trees, and
neural networks, which have been successfully attacked by prior work if not
attached with any defenses. We present a formal study of MI attacks by devising
a rigorous game-based definition and quantifying the associated information
leakage. Our theoretical analysis sheds light on the inefficacy of DP in
defending against MI attacks, which has been empirically observed in several
prior works. Our experiments demonstrate that MID leads to state-of-the-art
performance for a variety of MI attacks, target models and datasets.
