A Joint Exponential Mechanism for Differentially Private Top-k Set

We present a novel differentially private algorithm for releasing the set of k elements with the highest counts from a data domain of d elements. We define a ``joint'' instance of the exponential mechanism (EM) whose output space consists of all O(d^k) size-k subsets; yet, we are able to show how to sample from this EM in only time O(dk^3). Experiments suggest that this joint approach can yield utility improvements over the existing state of the art for small problem sizes.