On Low-Risk Heavy Hitters and Sparse Recovery Schemes

TL;DR

This paper advances the understanding of low-failure probability heavy hitters and sparse recovery, correcting prior analysis errors and introducing new algorithms with bounds for these problems.

Contribution

It corrects previous analysis errors, and presents new non-adaptive and adaptive sparse recovery algorithms with bounds for low-failure probability regimes.

Findings

Improved sparse recovery algorithms for low failure probability

Upper and lower bounds for heavy hitters with low failure probability

Correction of analysis errors in prior work

Abstract

We study the heavy hitters and related sparse recovery problems in the low-failure probability regime. This regime is not well-understood, and has only been studied for non-adaptive schemes. The main previous work is one on sparse recovery by Gilbert et al.(ICALP'13). We recognize an error in their analysis, improve their results, and contribute new non-adaptive and adaptive sparse recovery algorithms, as well as provide upper and lower bounds for the heavy hitters problem with low failure probability.