Maximum Mutual Information under Local Differential Privacy Constraint

Local differential privacy (LDP) is a state-of-the-art technique for privacy preservation. In this paper, we provide upper bounds for mutual information, a common information-theoretic metric, under pure LDP and approximate LDP constraints. Compared to existing results, our results have the advantage of holding for any discrete distribution and any privacy budget, and are tighter over some regions of the distribution and privacy budget.