# Differentially Private Approximate Quantiles

ICML 2022

## Abstract

In this work we study the problem of differentially private (DP) quantiles, in which given data $X$ set and quantiles $q_1, ..., q_m \in [0,1]$, we want to output $m$ quantile estimations such that the estimation is as close as possible to the optimal solution and preserves DP. In this work we provide \algoname~(AQ), an algorithm and implementation for the DP-quantiels problem. We analyze our algorithm and provide a mathematical proof of its error bounds for the general case and for the concrete case of uniform quantiles utility. We also experimentally evaluate \algoref~and conclude that it obtains higher accuracy than the existing baselines while having lower run time. We reduce the problem of DP-data-sanitization to the DP-uniform-quantiles problem and analyze the resulting mathematical bounds for the error in this case. We analyze our algorithm under the definition of zero Concentrated Differential Privacy (zCDP), and supply the error guarantees of our \algoref~in this case. Finally, we show the empirical benefit our algorithm gains under the zCDP definition.