Fast Private Kernel Density Estimation via Locality Sensitive Quantization

TL;DR

This paper introduces a fast, differentially private kernel density estimation method that operates efficiently in high-dimensional spaces by leveraging a new framework called Locality Sensitive Quantization, improving upon prior exponential-time algorithms.

Contribution

The paper presents LSQ, a novel framework enabling efficient private KDE approximation in high dimensions by privatizing existing non-private KDE techniques in a black-box manner.

Findings

Achieves linear time complexity in data dimensions for high-dimensional KDE.

Provides improved bounds for low-dimensional KDE.

Demonstrates fast and accurate performance on large datasets.

Abstract

We study efficient mechanisms for differentially private kernel density estimation (DP-KDE). Prior work for the Gaussian kernel described algorithms that run in time exponential in the number of dimensions $d$. This paper breaks the exponential barrier, and shows how the KDE can privately be approximated in time linear in $d$, making it feasible for high-dimensional data. We also present improved bounds for low-dimensional data. Our results are obtained through a general framework, which we term Locality Sensitive Quantization (LSQ), for constructing private KDE mechanisms where existing KDE approximation techniques can be applied. It lets us leverage several efficient non-private KDE methods -- like Random Fourier Features, the Fast Gauss Transform, and Locality Sensitive Hashing -- and ``privatize'' them in a black-box manner. Our experiments demonstrate that our resulting DP-KDE mechanisms are fast and accurate on large datasets in both high and low dimensions.