Nathan Srebro (Toyota Technological Institute at Chicago)

Matrix learning: a tale of two norms
Joint work with Rina Foygel, Jason Lee, Ben Recht, Russ Salakhutdinov, Ohad Shamir, Adi Shraibman and Joel Tropp and others.
Wednesday 23 May 2012 at 15.30, JCMB 6206

Abstract

There has been much interest in recent years in various ways of constraining the complexity of matrices based on factorizations into a product of two simpler matrices. Such measures of matrix complexity can then be used as regularizers for such tasks as matrix completion, collaborative filtering, multi-task learning and multi-class learning. In this talk I will discuss two forms of matrix regularization which constrain the norm of the factorization, namely the trace-norm (aka nuclear-norm) and the so-called max-norm (aka γ2:l1→l norm). I will both argue that they are independently motivated and often better model data then rank constraints, as well as explore their relationships to the rank. In particular, I will discuss how simple low-rank matrix completion guarantees can be obtained using these measures, and without various "incoherence" assumptions. I will present both theoretical and empirical arguments for why the max-norm might actually be a better regularizer, as well as a better convex surrogate for the rank.

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