Differentially Private Histograms under Continual Observation: Streaming Selection into the Unknown

We generalize the continuous observation privacy setting from Dwork et al. and Chan et al. by allowing each event in a stream to be a subset of some (possibly unknown) universe of items. We design differentially private (DP) algorithms for histograms in several settings, including top-k selection, with privacy loss that scales with polylog(T), where T is the maximum length of the input stream. We present a meta-algorithm that can use existing one-shot top-k private algorithms as a subroutine to continuously release DP histograms from a stream. Further, we present more practical DP algorithms for two settings: 1) continuously releasing the top-k counts from a histogram over a known domain when an event can consist of an arbitrary number of items, and 2) continuously releasing histograms over an unknown domain when an event has a limited number of items.