A Tight Analysis of Hutchinson's Diagonal Estimator

Previous chapter Next chapter Full AccessProceedings Symposium on Simplicity in Algorithms (SOSA)A Tight Analysis of Hutchinson's Diagonal EstimatorPrathamesh Dharangutte and Christopher MuscoPrathamesh Dharangutte and Christopher Muscopp.353 - 364Chapter DOI:https://doi.org/10.1137/1.9781611977585.ch32PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Let A ∈ ℝn×n be a matrix with diagonal diag(A) ∈ℝn. We show that the simple and practically popular Hutchinson's estimator, run for m trials, returns a diagonal estimate such that with probability 1 — δ Above c is a fixed constant and Ā equals A with its diagonal set to zero. This result improves on recent work in [4] by a log(n) factor, yielding a bound that is independent of the matrix dimension, n. We show a similar bound for variants of Hutchinson's estimator that use non-Rademacher random vectors. Previous chapter Next chapter RelatedDetails Published:2023eISBN:978-1-61197-758-5 https://doi.org/10.1137/1.9781611977585Book Series Name:ProceedingsBook Code:SOSA23Book Pages:vi + 389