  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.
