Differentially Private Fractional Frequency Moments Estimation with Polylogarithmic Space

Lun Wang, Iosif Pinelis, Dawn Song

Keywords: Differential Privacy, Fractional Frequency Moments

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. The code for evaluation is included in the supplementary material.

One-sentence Summary: We prove that $\mathbb{F}_p$ sketch, a well-celebrated streaming algorithm for frequency moments estimation, is differentially private as is when $p\in(0, 1]$.