Flexible Low-Rank Statistical Modeling with Side Information
This work provides a flexible approach for statistical modeling with side information, generalizing existing methods like matrix completion and Bayesian models, but it appears incremental as it builds on prior convex and hierarchical techniques.
The authors tackled the problem of reduced-rank modeling of matrix-valued data by proposing a general framework that incorporates side information through a generalized nuclear norm penalty, enabling scalable estimation via convex optimization with one SVD per iteration.
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.