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Matrix reconstruction with the local max norm
Rina Foygel · Nati Srebro · Russ Salakhutdinov

Tue Dec 04 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor

We introduce a new family of matrix norms, the ''local max'' norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the literature as regularizers for matrix reconstruction problems. We show that this new family can be used to interpolate between the (weighted or unweighted) trace norm and the more conservative max norm. We test this interpolation on simulated data and on the large-scale Netflix and MovieLens ratings data, and find improved accuracy relative to the existing matrix norms. We also provide theoretical results showing learning guarantees for some of the new norms.

Author Information

Rina Foygel (Stanford University)
Nati Srebro (TTI-Chicago)
Russ Salakhutdinov (Carnegie Mellon University)

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