On the Sample Complexity of Compressed Counting

TL;DR

This paper introduces a simple algorithm for estimating frequency moments in data streams, significantly improving sample complexity bounds, especially for Shannon entropy estimation, based on compressed counting techniques.

Contribution

It presents a new simple algorithm using the sample minimum estimator and proves improved sample complexity bounds for compressed counting.

Findings

Enhanced sample complexity bounds for frequency moment estimation.

Effective estimation of Shannon entropy in data streams.

Simplified algorithm based on the sample minimum estimator.

Abstract

Compressed Counting (CC), based on maximally skewed stable random projections, was recently proposed for estimating the p-th frequency moments of data streams. The case p->1 is extremely useful for estimating Shannon entropy of data streams. In this study, we provide a very simple algorithm based on the sample minimum estimator and prove a much improved sample complexity bound, compared to prior results.