Primal-Dual methods for sparse constrained matrix completion

We develop scalable algorithms for regular and non-negative matrix completion. In particular, we base the methods on trace-norm regularization that induces a low rank predicted matrix. The regularization problem is solved via a constraint generation method that explicitly maintains a sparse dual and the corresponding low rank primal solution. We provide a new dual block coordinate descent algorithm for solving the dual problem with a few spectral constraints. Empirical results illustrate the effectiveness of our method in comparison to recently proposed alternatives.

• Type: Journal
• Year: 2012
• Where: JMLR
• Authors: Yu Xin, Tommi Jaakkola
• Keywords: Constraint Generation, JMLR 2012, Primal Solution, Programming Languages, Spectral Constraints