Scaled stochastic gradient descent for low-rank matrix completion
This addresses the issue of scale invariance in matrix factorization models for large-scale applications, though it appears incremental.
The paper tackles the matrix completion problem by introducing a scaled variant of stochastic gradient descent that uses matrix-scaling as preconditioning, resulting in competitive performance with state-of-the-art algorithms on benchmarks.
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.