Private Counting of Distinct and k-Occurring Items in Time Windows

TL;DR

This paper develops differentially private algorithms for counting distinct and k-occurring items in time windows, providing tight bounds and answering an open question on error bounds for recent item counts.

Contribution

It introduces nearly tight bounds for DP algorithms in various window and neighbor models, and presents an event-level DP algorithm with polylogarithmic error for recent item counts.

Findings

Nearly tight bounds for DP errors in different window models

An event-level DP algorithm with polylogarithmic error for recent counts

Answers an open question from ICDT 2013 about error bounds

Abstract

In this work, we study the task of estimating the numbers of distinct and $k$-occurring items in a time window under the constraint of differential privacy (DP). We consider several variants depending on whether the queries are on general time windows (between times $t_1$ and $t_2$), or are restricted to being cumulative (between times $1$ and $t_2$), and depending on whether the DP neighboring relation is event-level or the more stringent item-level. We obtain nearly tight upper and lower bounds on the errors of DP algorithms for these problems. En route, we obtain an event-level DP algorithm for estimating, at each time step, the number of distinct items seen over the last $W$ updates with error polylogarithmic in $W$; this answers an open question of Bolot et al. (ICDT 2013).