Sublinear Space Private Algorithms Under the Sliding Window Model

The Differential privacy overview of Apple states, ``Apple retains the collected data for a maximum of three months." Analysis of recent data is formalized by the {\em sliding window model}. This begs the question: what is the price of privacy in the {sliding window model}. In this paper, we study heavy hitters in the sliding window model with window size $w$. Previous works of~\citet{chan2012differentially} estimates heavy hitters using $O(w)$ space and incur an error of order $\theta w$ for a constant $\theta >0$. In this paper, we give an efficient differentially private algorithm to estimate heavy hitters in the sliding window model with $\widetilde O(w^{3/4})$ additive error and using $\widetilde O(\sqrt{w})$ space.