A Joint Exponential Mechanism For Differentially Private Top-$k$

TL;DR

This paper introduces a new differentially private algorithm for releasing the top-$k$ elements with high counts, using a joint exponential mechanism that is more efficient and effective than previous methods.

Contribution

The paper proposes a novel joint exponential mechanism for differential privacy that efficiently samples top-$k$ sequences with improved accuracy over existing methods.

Findings

Outperforms existing pure differential privacy methods.

Improves upon approximate differential privacy approaches for moderate $k$.

Efficient sampling in time $O(dk\log(k) + d\log(d))$ and space $O(dk)$.

Abstract

We present a differentially private algorithm for releasing the sequence of $k$ elements with the highest counts from a data domain of $d$ elements. The algorithm is a "joint" instance of the exponential mechanism, and its output space consists of all $O(d^k)$ length-$k$ sequences. Our main contribution is a method to sample this exponential mechanism in time $O(dk\log(k) + d\log(d))$ and space $O(dk)$. Experiments show that this approach outperforms existing pure differential privacy methods and improves upon even approximate differential privacy methods for moderate $k$.