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While most work on differential privacy has focused on protecting the privacy of tuples, it has been realized that such a simple model cannot capture the complex user-tuple relationships in many real-world applications. Thus, user differential privacy (user-DP) has recently gained more attention, which includes node-DP for graph data as a special case. Most existing work on user-DP has only studied the sum estimation problem. In this work, we design a general DP mechanism for any monotonic function under user-DP with strong optimality guarantees. While our general mechanism may run in super-polynomial time, we show how to instantiate an approximate version in polynomial time on some common monotonic functions, including sum, k-selection, maximum frequency, and distinct count. Finally, we conduct experiments on all these functions and the results show that our framework is more general and obtains better results in many cases.
Fang et al. (Mon,) studied this question.