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In this work, we study the problem of privately maximizing a submodular function in the streaming setting. Extensive work has been done on privately maximizing submodular functions in the general case when the function depends upon the private data of individuals. However, when the size of the data stream drawn from the domain of the objective function is large or arrives very fast, one must privately optimize the objective within the constraints of the streaming setting. We establish fundamental differentially private baselines for this problem and then derive better trade-offs between privacy and utility for the special case of decomposable submodular functions. A submodular function is decomposable when it can be written as a sum of submodular functions; this structure arises naturally when each summand function models the utility of an individual and the goal is to study the total utility of the whole population as in the well-known Combinatorial Public Projects Problem. Finally, we complement our theoretical analysis with experimental corroboration. 

This paper studies the problem of clustering in metric spaces while preserving the privacy of individual data. Specifically, we examine differentially private variants of the k-medians and Euclidean k-means problems. We present polynomial algorithms with constant multiplicative error and lower additive error than the previous state-of-the-art for each problem. Additionally, our algorithms use a clustering algorithm without differential privacy as a black-box. This allows practitioners to control the trade-off between runtime and approximation factor by choosing a suitable clustering algorithm to use.