Collaborative Filtering in a Non-Uniform World: Learning with the Weighted Trace Norm

We show that matrix completion with trace-norm regularization can be significantly hurt when entries of the matrix are sampled non-uniformly, but that a properly weighted version of the trace-norm regularizer works well with non-uniform sampling. We show that the weighted trace-norm regularization indeed yields significant gains on the highly non-uniformly sampled Netflix dataset. Papers published at the Neural Information Processing Systems Conference.