Robust matrix factorization (RMF), which uses the $\ell_1$-loss, often outperforms standard matrix factorization using the $\ell_2$-loss, particularly when outliers are present. The state-of-the-art RMF solver is the RMF-MM algorithm, which, however, cannot utilize data sparsity. Moreover, sometimes even the (convex) $\ell_1$-loss is not robust enough. In this paper, we propose the use of nonconvex loss to enhance robustness. To address the resultant difficult optimization problem, we use majorization-minimization (MM) optimization and propose a new MM surrogate. To improve scalability, we exploit data sparsity and optimize the surrogate via its dual with the accelerated proximal gradient algorithm. The resultant algorithm has low time and space complexities and is guaranteed to converge to a critical point. Extensive experiments demonstrate its superiority over the state-of-the-art in terms of both accuracy and scalability.

By exploiting students' response logs, SCM aims to predict their exercise

Our framework applies to a wide range of SMF-type problems for multi-class classification with auxiliary features.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Because of the ubiquitous applications of NMF, many efficient algorithms have been proposedforsolving(1).

Neural Information Processing Systems http://nips.cc/

On the theory side, most of the existing works have focused on algorithm design.

On the theory side, most of the existing works have focused on algorithm design.