Scaled stochastic gradient descent for low-rank matrix completion

TL;DR

This paper introduces a scaled stochastic gradient descent method with a novel matrix-scaling preconditioning for efficient, large-scale low-rank matrix completion, improving convergence and scale invariance handling.

Contribution

It proposes a new matrix-scaling technique for stochastic gradient descent that enhances performance and scalability in matrix completion tasks.

Findings

Competitive performance on benchmark datasets

Linear computational complexity with data size

Effective handling of scale invariance issues

Abstract

The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the standard stochastic gradient descent algorithm. This proposed matrix-scaling provides a trade-off between local and global second order information. It also resolves the issue of scale invariance that exists in matrix factorization models. The overall computational complexity is linear with the number of known entries, thereby extending to a large-scale setup. Numerical comparisons show that the proposed algorithm competes favorably with state-of-the-art algorithms on various different benchmarks.