Sparse Group Inductive Matrix Completion

Abstract

We consider the problem of matrix completion with side information (inductive matrix completion). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the problem. We incorporate feature selection into inductive matrix completion by proposing a matrix factorization framework with group-lasso regularization on side feature parameter matrices. We demonstrate, that the theoretical sample complexity for the proposed method is much lower compared to its competitors in sparse problems, and propose an efficient optimization algorithm for the resulting low-rank matrix completion problem with sparsifying regularizers. Experiments on synthetic and real-world datasets show that the proposed approach outperforms other methods.

Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion

“…Our work differs from the attempts in Lu et al (2016), Soni et al (2016), andNazarov et al (2018) as it does not consider the heuristic convex relaxation of sparsity in the nuclear norm, but rather the exact sparse problem. Different to Bertsimas and Li (2018) where the underlying rank vectors need to be an exact vector given in the side information, we relax such assumption and allow the rank vectors to be formed by any linear combination of the vectors contained in the side information.…”

“…Chiang et al (2015) explored the case in which the side information is corrupted with noise, while Shah et al (2017) and Si et al (2016) incorporated nonlinear combination of factors into the side information. As pointed out by a recent article Nazarov et al (2018), there is a considerable lack of effort to introduce sparsity into inductive matrix completion, with Lu et al (2016), Soni et al (2016), Nazarov et al (2018) as examples. Recently, in Bertsimas and Li (2018), the authors introduced a convex binary formulation of the sparse inductive matrix completion problem, and constructed randomized algorithms for scaling.…”

“…In recent years, as noted by Nazarov et al (2018), there has been a rise in interest for inductive matrix completion, where the common linear factors are chosen from a set of given vectors in the form of side information.…”

Recommender Systems in Antiviral Drug Discovery

“…To complete the antiviral activity matrix, we used the CF algorithm implemented in Surprise package 51 and sparse-group inductive matrix completion (SGIMC) implementation of CBF. 52 Several questions were addressed in our study: (1) Are the RS approaches effective in the context of antiviral activity prediction taking into account the data sparsity and unusual complexity of targets (viruses)? (2) Which RS approach gives a more accurate prediction?…”

Interpretable Matrix Completion: A Discrete Optimization Approach

“…For example, in the original Netflix 3 of factors into the side information. Surprisingly, as pointed out by a recent article Nazarov et al (2018), there is a considerable lack of effort to introduce sparsity into inductive matrix completion, with Lu et al (2016), Soni et al (2016) and Nazarov et al (2018) being among the only works that attempt to do so. Our work differs from the previous attempts to introduce sparsity in that it does not consider the heuristic convex relaxation of sparsity in the nuclear norm.…”