A Tight Analysis of Hutchinson's Diagonal Estimator

Prathamesh Dharangutte, Christopher Musco

Abstract: 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.