ACCAMS: Additive Co-Clustering to Approximate Matrices Succinctly

Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple insight that an additive model of co-clusterings allows one to approximate matrices efficiently. This allows us to build a concise model that, per bit of model learned, significantly beats all factorization approaches in matrix completion. Even more surprisingly, we find that summing over small co-clusterings is more effective in modeling matrices than classic co-clustering, which uses just one large partitioning of the matrix. Following Occam's razor principle, the fact that our model is more concise and yet just as accurate as more complex models suggests that it better captures the latent preferences and decision making processes present in the real world. We provide an iterative minimization algorithm, a collapsed Gibbs sampler, theoretical guarantees for matrix approximation, and excellent empirical evidence for the efficacy of our approach. We achieve state-of-the-art results for matrix completion on Netflix at a fraction of the model complexity.