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Differentially Private Continual Release of Histograms and Related Queries by Henzinger, Monika; Sricharan, A. R.; Steiner, Teresa Anna is a scholarly article available to read on EtoBox.

What is Differentially Private Continual Release of Histograms and Related Queries about?

We study privately releasing column sums of a $d$-dimensional table with entries from a universe $\chi$ undergoing $T$ row updates, called histogram under continual release. Our mechanisms give better additive $\ell_\infty$-error than existing mechanisms for a large class of queries and input streams. Our first contribution is an output-sensitive mechanism in the insertions-only model ($\chi = \{0,1\}$) for maintaining (i) the histogram or (ii) queries that do not require maintaining the entire histogram, such as the maximum or minimum column sum, the median, or any quantiles. The mechanism has an additive error of $O(d\log^2 (dq^*)+\log T)$ whp, where $q^*$ is the maximum output value over all time steps on this dataset. The mechanism does not require $q^*$ as input. This breaks the $\Omega(d \log T)$ bound of prior work when $q^* \ll T$. Our second contribution is a mechanism for the turnstile model that admits negative entry updates ($\chi = \{-1, 0,1\}$). This mechanism has an additive error of $O(d \log^2 (dK) + \log T)$ whp, where $K$ is the number of times two consecutive data rows differ, and the mechanism does not require $K$ as input. This is useful when monitoring inputs

Author

Henzinger, Monika; Sricharan, A. R.; Steiner, Teresa Anna

Published

2023

Language

EN