Faster Differentially Private Top-$k$ Selection: A Joint Exponential Mechanism with Pruning

TL;DR

This paper introduces a faster differentially private top-$k$ selection algorithm that maintains high accuracy while significantly reducing computational complexity, making it more practical for large datasets.

Contribution

The authors propose a novel joint exponential mechanism with pruning, improving time and space complexity from previous methods while preserving empirical accuracy.

Findings

Our algorithm is orders of magnitude faster than previous approaches.

It achieves similar empirical accuracy despite reduced complexity.

The method is scalable to larger datasets with high-dimensional data.

Abstract

We study the differentially private top-$k$ selection problem, aiming to identify a sequence of $k$ items with approximately the highest scores from $d$ items. Recent work by Gillenwater et al. (ICML '22) employs a direct sampling approach from the vast collection of $d^{\,\Theta(k)}$ possible length-$k$ sequences, showing superior empirical accuracy compared to previous pure or approximate differentially private methods. Their algorithm has a time and space complexity of $\tilde{O}(dk)$. In this paper, we present an improved algorithm with time and space complexity $O(d + k^2 / \epsilon \cdot \ln d)$, where $\epsilon$ denotes the privacy parameter. Experimental results show that our algorithm runs orders of magnitude faster than their approach, while achieving similar empirical accuracy.