  Privacy against an adversary (AD) that tries to detect the underlying
privacy-sensitive data distribution is studied. The original data sequence is
assumed to come from one of the two known distributions, and the privacy
leakage is measured by the probability of error of the binary hypothesis test
carried out by the AD. A management unit (MU) is allowed to manipulate the
original data sequence in an online fashion, while satisfying an average
distortion constraint. The goal of the MU is to maximize the minimal type II
probability of error subject to a constraint on the type I probability of error
assuming an adversarial Neyman-Pearson test, or to maximize the minimal error
probability assuming an adversarial Bayesian test. The asymptotic exponents of
the maximum minimal type II probability of error and the maximum minimal error
probability are shown to be characterized by a Kullback-Leibler divergence rate
and a Chernoff information rate, respectively. Privacy performances of
particular management policies, the memoryless hypothesis-aware policy and the
hypothesis-unaware policy with memory, are compared. The proposed formulation
can also model adversarial example generation with minimal data manipulation to
fool classifiers. Lastly, the results are applied to a smart meter privacy
problem, where the user's energy consumption is manipulated by adaptively using
a renewable energy source in order to hide user's activity from the energy
provider.
