Orthogonal Inductive Matrix Completion

We propose orthogonal inductive matrix completion (OMIC), an interpretable approach to inductive matrix completion based on a sum of multiple orthonormal side information terms, together with nuclear-norm regularization. The approach allows us to inject prior knowledge about the eigenvectors of the ground truth matrix. We optimize the approach by a provably converging algorithm, which optimizes all components of the model simultaneously. Our method enjoys distribution-free learning guarantees that improve with the quality of the injected knowledge. As a special case of our general framework, we study a model consisting of a sum of user and item biases (generic behavior), a non-inductive term (specific behavior), and (optionally) an inductive term using side information. Our theoretical analysis shows that $\epsilon$-recovering a ground truth matrix in $\mathbb{R}^{m\times n}$ requires at most $O\left( \frac{n+m+(\sqrt{n}+\sqrt{m}) \sqrt{mnr}C}{\epsilon^2}\right)$ entries, where $r$ (resp. $C$) is the rank (resp. maximum entry) of the bias-free part of the ground truth matrix. We analyse the performance of OMIC on several synthetic and real datasets. On synthetic datasets with a sliding scale of user bias relevance, we show that OMIC better adapts to different regimes than other methods. On real-life datasets containing user/items recommendations and relevant side information, we find that OMIC surpasses the state-of-the-art, with the added benefit of greater interpretability.