Understanding Compressive Adversarial Privacy

Designing a data sharing mechanism without sacrificing too much privacy can be considered as a game between data holders and malicious attackers. This paper describes a compressive adversarial privacy framework that captures the trade-off between the data privacy and utility. We characterize the optimal data releasing mechanism through convex optimization when assuming that both the data holder and attacker can only modify the data using linear transformations. We then build a more realistic data releasing mechanism that can rely on a nonlinear compression model while the attacker uses a neural network. We demonstrate in a series of empirical applications that this framework, consisting of compressive adversarial privacy, can preserve sensitive information

Extremal Mechanisms for Local Differential Privacy

Local differential privacy has recently surfaced as a strong measure of privacy in contexts where personal information remains private even from data analysts. Working in a setting where both the data providers and data analysts want to maximize the utility of statistical analyses performed on the released data, we study the fundamental trade-off between local differential privacy and utility. This trade-off is formulated as a constrained optimization problem: maximize utility subject to local differential privacy constraints. We introduce a combinatorial family of extremal privatization mechanisms, which we call staircase mechanisms, and show that it contains the optimal privatization mechanisms for a broad class of information theoretic utilities such as mutual information and $f$-divergences. We further prove that for any utility function and any privacy level, solving the privacy-utility maximization problem is equivalent to solving a finite-dimensional linear program, the outcome of which is the optimal staircase mechanism. However, solving this linear program can be computationally expensive since it has a number of variables that is exponential in the size of the alphabet the data lives in. To account for this, we show that two simple privatization mechanisms, the binary and randomized response mechanisms, are universally optimal in the low and high privacy regimes, and well approximate the intermediate regime.Comment: 52 pages, 10 figures in JMLR 201