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Privacy against an adversary (AD) that tries to detect the underlyingprivacy-sensitive data distribution is studied. The original data sequence isassumed to come from one of the two known distributions, and the privacyleakage is measured by the probability of error of the binary hypothesis testcarried out by the AD. A management unit (MU) is allowed to manipulate theoriginal data sequence in an online fashion, while satisfying an averagedistortion constraint. The goal of the MU is to maximize the minimal type IIprobability of error subject to a constraint on the type I probability of errorassuming an adversarial Neyman-Pearson test, or to maximize the minimal errorprobability assuming an adversarial Bayesian test. The asymptotic exponents ofthe maximum minimal type II probability of error and the maximum minimal errorprobability are shown to be characterized by a Kullback-Leibler divergence rateand a Chernoff information rate, respectively. Privacy performances ofparticular management policies, the memoryless hypothesis-aware policy and thehypothesis-unaware policy with memory, are compared. The proposed formulationcan also model adversarial example generation with minimal data manipulation tofool classifiers. Lastly, the results are applied to a smart meter privacyproblem, where the user's energy consumption is manipulated by adaptively usinga renewable energy source in order to hide user's activity from the energyprovider.

Privacy against a Hypothesis Testing Adversary