Private testing of distributions via sample permutations

Statistical tests are at the heart of many scientific tasks. To validate their hypotheses, researchers in medical and social sciences use individuals' data. The sensitivity of participants' data requires the design of statistical tests that ensure the privacy of the individuals in the most efficient way. In this paper, we use the framework of property testing to design algorithms to test the properties of the distribution that the data is drawn from with respect to differential privacy. In particular, we investigate testing two fundamental properties of distributions: (1) testing the equivalence of two distributions when we have unequal numbers of samples from the two distributions. (2) Testing independence of two random variables. In both cases, we show that our testers achieve near optimal sample complexity (up to logarithmic factors). Moreover, our dependence on the privacy parameter is an additive term, which indicates that differential privacy can be obtained in most regimes of parameters for free.