A Modern Analysis of Hutchinson's Trace Estimator

TL;DR

This paper advances the understanding of Hutchinson's trace estimator by introducing novel analytical tools, resulting in more accurate bounds and promoting these techniques within the computer science community.

Contribution

It provides a new, modular analysis using hypercontractive inequalities and sub-gamma concentration, achieving state-of-the-art accuracy bounds for Hutchinson's estimator.

Findings

Numerically superior bounds for trace estimation accuracy.

Introduction of hypercontractive inequalities in the analysis.

Enhanced understanding of concentration properties in trace estimation.

Abstract

The paper establishes the new state-of-art in the accuracy analysis of Hutchinson's trace estimator. Leveraging tools that have not been previously used in this context, particularly hypercontractive inequalities and concentration properties of sub-gamma distributions, we offer an elegant and modular analysis, as well as numerically superior bounds. Besides these improvements, this work aims to better popularize the aforementioned techniques within the CS community.