Differentially Private Fractional Frequency Moments Estimation with Polylogarithmic Space

TL;DR

This paper demonstrates that the $ ext{F}_p$ sketch algorithm for frequency moments estimation is differentially private with polylogarithmic space, offering a significant efficiency improvement over existing methods while maintaining reasonable accuracy.

Contribution

It proves differential privacy for the $ ext{F}_p$ sketch in the range p∈(0,1], achieving polylogarithmic space complexity and outperforming prior private algorithms.

Findings

$ ext{F}_p$ sketch is differentially private for p∈(0,1].

The algorithm uses only polylogarithmic space.

It achieves accuracy close to non-private baselines.

Abstract

We prove that $\mathbb{F}_p$ sketch, a well-celebrated streaming algorithm for frequency moments estimation, is differentially private as is when $p\in(0, 1]$. $\mathbb{F}_p$ sketch uses only polylogarithmic space, exponentially better than existing DP baselines and only worse than the optimal non-private baseline by a logarithmic factor. The evaluation shows that $\mathbb{F}_p$ sketch can achieve reasonable accuracy with strong privacy guarantees.