On computing approximate Lewis weights
arxiv(2024)
摘要
In this note we provide and analyze a simple method that given an n ×
d matrix, outputs approximate ℓ_p-Lewis weights, a natural measure of the
importance of the rows with respect to the ℓ_p norm, for p ≥ 2. More
precisely, we provide a simple post-processing procedure that turns natural
one-sided approximate ℓ_p-Lewis weights into two-sided approximations.
When combined with a simple one-sided approximation algorithm presented by Lee
(PhD thesis, `16) this yields an algorithm for computing two-sided
approximations of the ℓ_p-Lewis weights of an n × d-matrix using
poly(d,p) approximate leverage score computations. While efficient
high-accuracy algorithms for approximating ℓ_p-Lewis had been established
previously by Fazel, Lee, Padmanabhan and Sidford (SODA `22), the simple
structure and approximation tolerance of our algorithm may make it of use for
different applications.
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