We study membership inference in settings where assumptions commonly used in previous research are relaxed. First, we consider cases where only a small fraction of the candidate pool targeted by the adversary are members and develop a PPV-based metric suitable for this setting. This skewed prior setting is more realistic than the balanced prior setting typically considered. Second, we consider adversaries that select inference thresholds according to their attack goals, such as identifying as many members as possible with a given false positive tolerance. We develop a threshold selection designed for achieving particular attack goals. Since previous inference attacks fail in imbalanced prior settings, we develop new inference attacks based on the intuition that inputs corresponding to training set members will be near a local minimum in the loss function. An attack that combines this with thresholds on the per-instance loss can achieve high PPV even in settings where other attacks are ineffective.

While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains under challenging. In this paper, we study nonconvex ERM, which takes the form of minimizing a finite-sum of nonconvex loss functions over a training set. To achieve both efficiency and strong privacy guarantees with efficiency, we propose a differentially-private stochastic gradient descent algorithm for nonconvex ERM, and provide a tight analysis of its privacy and utility guarantees, as well as its gradient complexity. We show that our proposed algorithm can substantially reduce gradient complexity while matching the best-known utility guarantee obtained by Wang et al. (2017). We extend our algorithm to the distributed setting using secure multi-party computation, and show that it is possible for a distributed algorithm to match the privacy and utility guarantees of a centralized algorithm in this setting. Our experiments on benchmark nonconvex ERM problems and real datasets demonstrate superior performance in terms of both training time and utility gains compared with previous differentially-private methods using the same privacy budgets.

Membership inference attacks on models trained using machine learning have been shown to pose significant privacy risks. However, previous works on membership inference assume a balanced prior distribution where the adversary randomly chooses target records from a pool that has equal numbers of members and nonmembers. Such an assumption of balanced prior is unrealistic in practical scenarios. This paper studies membership inference attacks under more realistic assumptions. First, we consider skewed priors where a non-member is more likely to occur than a member record. For this, we use metric based on positive predictive value (PPV) in conjunction with membership advantage for privacy leakage evaluation, since PPV considers the prior. Second, we consider adversaries that can select inference thresholds according to their attack goals. For this, we develop a threshold selection procedure that improves inference attacks. We also propose a new membership inference attack called Merlin which outperforms previous attacks. Our experimental evaluation shows that while models trained without privacy mechanisms are vulnerable to membership inference attacks in balanced prior settings, there appears to be negligible privacy risk in the skewed prior setting.

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