Escaping Saddle Points in Ill-Conditioned Matrix Completion with a Scalable Second Order Method
Abstract
We propose an iterative algorithm for low-rank matrix completion that can be interpreted as both an iteratively reweighted least squares (IRLS) algorithm and a saddle-escaping smoothing Newton method applied to a non-convex rank surrogate objective. It combines the favorable data efficiency of previous IRLS approaches with an improved scalability by several orders of magnitude. Our method attains a local quadratic convergence rate already for a number of samples that is close to the information theoretical limit. We show in numerical experiments that unlike many state-of-the-art approaches, our approach is able to complete very ill-conditioned matrices with a condition number of up to from few samples.
Cite
@article{arxiv.2009.02905,
title = {Escaping Saddle Points in Ill-Conditioned Matrix Completion with a Scalable Second Order Method},
author = {Christian Kümmerle and Claudio M. Verdun},
journal= {arXiv preprint arXiv:2009.02905},
year = {2020}
}
Comments
15 pages, presented at the Workshop on "Beyond first-order methods in ML systems" at the $37^th$ International Conference on Machine Learning (ICML), Vienna, Austria, 2020