Convergence Rates for Greedy Kaczmarz Algorithms, and Faster Randomized Kaczmarz Rules Using the Orthogonality Graph

View Researcher II's Other Codes

Disclaimer: The provided code links for this paper are external links. Science Nest has no responsibility for the accuracy, legality or content of these links. Also, by downloading this code(s), you agree to comply with the terms of use as set out by the author(s) of the code(s).

Please contact us in case of a broken link from here

Authors Julie Nutini, Behrooz Sepehry, Issam H. Laradji, Mark W. Schmidt, Hoyt A. Koepke
Journal/Conference Name Uncertainty in Artificial Intelligence
Paper Category
Paper Abstract The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a non-asymptotic convergence rate analysis for this algorithm, spurring numerous extensions and generalizations of the Kaczmarz method. Rather than the randomized selection rule analyzed in that work, in this paper we instead discuss greedy and approximate greedy selection rules. We show that in some applications the computational costs of greedy and random selection are comparable, and that in many cases greedy selection rules give faster convergence rates than random selection rules. Further, we give the first multi-step analysis of Kaczmarz methods for a particular greedy rule, and propose a provably-faster randomized selection rule for matrices with many pairwise-orthogonal rows.
Date of publication 2016
Code Programming Language Python
Comment

Copyright Researcher II 2021