We study the problem of top-k selection over a large domain universe to user-level differential privacy. Typically, the exponential or report noisy max are the algorithms used to solve this problem., these algorithms require querying the database for the count of each element. We focus on the setting where the data domain is unknown, which different than the setting of frequent itemsets where an apriori type can help prune the space of domain elements to query. We design that ensures (approximate) (\ε,\δ>0)-differential and only needs access to the true top-̄ elements from the data any chosen ̄ \≥ k. This is a highly desirable feature for making privacy practical, since the algorithms require no knowledge of domain. We consider both the setting where a user's data can modify an number of counts by at most 1, i.e. unrestricted sensitivity, and the where a user's data can modify at most some small, fixed number of by at most 1, i.e. restricted sensitivity. Additionally, we provide a-what-you-get privacy composition bound for our algorithms. That is, our might return fewer than k elements when the top-k elements are, but the overall privacy budget only decreases by the size of the set.
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Durfee et al. (2019) studied this question.