Bounded Space Differentially PrivateQuantiles

Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile computation require space at least linear in the input sizen. In this work, we devise a differentially private algorithm for the quantile estimation problem with strongly sublinear space complexity. Our main mechanism estimates any α-approximate quantile of a length-n stream over a data universe X with probability 1 − β using O ( log( |X |/β) log(αεn)