  We propose a general framework for reduced-rank modeling of matrix-valued
data. By applying a generalized nuclear norm penalty we can directly model
low-dimensional latent variables associated with rows and columns. Our
framework flexibly incorporates row and column features, smoothing kernels, and
other sources of side information by penalizing deviations from the row and
column models. Moreover, a large class of these models can be estimated
scalably using convex optimization. The computational bottleneck in each case
is one singular value decomposition per iteration of a large but easy-to-apply
matrix. Our framework generalizes traditional convex matrix completion and
multi-task learning methods as well as maximum a posteriori estimation under a
large class of popular hierarchical Bayesian models.
