Distributed Hypothesis Testing with Privacy Constraints

We revisit the hypothesis testing with communication constraints problem, also called distributed hypothesis testing, from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized version of it. We impose an upper bound on the mutual information between the raw and randomized data. Under this scenario, the decoder, which is also provided with side information, is required to make a decision on whether the null or alternative hypothesis is in effect. First, we provide a general lower bound on the type-II exponent for arbitrary hypotheses, privacy mechanism, rates, and leakage parameters. Second, we consider the testing against independence scenario in which the distribution under the alternative hypothesis is the product of the marginals of the distribution under the null hypothesis. In this setup, we show that the exponent is known exactly and the strong converse property holds. Finally, the trade-offs between the exponent, compression rate, and leakage parameter are illustrated through a binary example.