Seminar Details

Seminar Details


Oct 22

3:30 pm

Low-rank matrix reconstruction with a new family of matrix norms

Rina Foygel


University of Chicago

We consider the problem of reconstructing a low-rank matrix from sparse observations and create a new family of norms, the "local max"
norms, generalizing many existing matrix norms that have been used as convex regularizers for this problem. This family of norms interpolates between the well-studied trace norm (nuclear norm) and the more conservative max norm regularizer, and generalizes the idea of the weighted trace norm, which has been used in applications where some areas of the matrix are more heavily sampled. We find new norms in this family that outperform existing matrix norms on the Netflix and MovieLens movie ratings data sets and on simulated data, and state some theoretical results for these new norms that give insight into their improved accuracy.