Distributed hypothesis testing under privacy constraints

A distributed binary hypothesis testing problem involving two parties, a remote observer and a detector, is studied. The remote observer has access to a discrete memoryless source, and communicates its observations to the detector via a rate-limited noiseless channel. The detector tests for the independence of its own observations with that of the observer, conditioned on some additional side information. While the goal is to maximize the type 2 error exponent of the test for a given type 1 error probability constraint, it is also desired to keep a private part, which is correlated with the observer's observations, as oblivious to the detector as possible. Considering equivocation and average distortion as the metrics of privacy at the detector, a tight single-letter characterization of the rate-error exponent-equivocation and rate-error exponent-distortion tradeoff is obtained.