  We generalize the continuous observation privacy setting from Dwork et al.
'10 and Chan et al. '11 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-$k$ DP algorithms as a subroutine to continuously release
private 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.
