  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 to
matrix approximation. 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 suggests that the simple structure induced
by our model better captures the latent preferences and decision making
processes present in the real world than classic co-clustering or matrix
factorization. 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 on the Netflix problem with a fraction of the model
complexity.
