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.

翻译：我们将Dwork et al. '10 和Chan et al.'11 的连续观察隐私设置概括化,允许流中的每一事件成为某些(可能未知的)项目宇宙的子集。我们设计了不同程度的私人(DP)算法,用于几种环境中的直方图,包括最高-美元选择,而隐私损失的尺度是多log$(T),其中$T是输入流的最大长度。我们提出了一个元算法,可以使用现有的一发最高-美元DP算法作为子路程,从流中持续释放私人直方图。此外,我们为两个设置了更实用的 DP算法:1) 当事件包含数量有限的项目时,持续释放一个已知域的直方图上-千美元计数,2) 当事件有数量有限的项目时,持续释放未知域的直方图。