Adversarially Robust Dense-Sparse Tradeoffs via Heavy-Hitters

TL;DR

This paper improves adversarially robust algorithms in streaming models by developing better heavy-hitter detection and frequency moment estimation techniques, leading to more efficient $L_p$ estimation under adversarial conditions.

Contribution

It introduces an improved adversarially robust heavy-hitter algorithm and a new tail frequency moment estimator, enhancing robustness and efficiency in streaming data analysis.

Findings

Enhanced heavy-hitter detection with deterministic algorithms.

Space-efficient tail frequency moment estimation with additive error.

Improved adversarially robust $L_p$ estimation algorithms.

Abstract

In the adversarial streaming model, the input is a sequence of adaptive updates that defines an underlying dataset and the goal is to approximate, collect, or compute some statistic while using space sublinear in the size of the dataset. In 2022, Ben-Eliezer, Eden, and Onak showed a dense-sparse trade-off technique that elegantly combined sparse recovery with known techniques using differential privacy and sketch switching to achieve adversarially robust algorithms for $L_p$ estimation and other algorithms on turnstile streams. In this work, we first give an improved algorithm for adversarially robust $L_p$-heavy hitters, utilizing deterministic turnstile heavy-hitter algorithms with better tradeoffs. We then utilize our heavy-hitter algorithm to reduce the problem to estimating the frequency moment of the tail vector. We give a new algorithm for this problem in the classical streaming setting, which achieves additive error and uses space independent in the size of the tail. We then leverage these ingredients to give an improved algorithm for adversarially robust $L_p$ estimation on turnstile streams.