Matrix reconstruction with the local max norm
This work addresses matrix reconstruction for applications like recommendation systems, but it appears incremental as it builds on existing norms.
The authors tackled the problem of matrix reconstruction by introducing a new family of matrix norms called 'local max' norms, which interpolate between trace and max norms, and found improved accuracy on simulated data and large-scale datasets like Netflix and MovieLens.
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.