Collaborative Filtering with the Trace Norm: Learning, Bounding, and Transducing
Ohad Shamir and Shai Shalev-Shwartz
In: COLT 2011, June 2011, Budapest, Hungary.

Abstract

Trace-norm regularization is a widely-used and successful approach for collaborative lter- ing and matrix completion. However, its theoretical understanding is surprisingly weak, and despite previous attempts, there are no distribution-free, non-trivial learning guaran- tees currently known. In this paper, we bridge this gap by providing such guarantees, under mild assumptions which correspond to collaborative ltering as performed in practice. In fact, we claim that previous diculties partially stemmed from a mismatch between the standard learning-theoretic modeling of collaborative ltering, and its practical applica- tion. Our results also shed some light on the issue of collaborative ltering with bounded models, which enforce predictions to lie within a certain range. In particular, we provide experimental and theoretical evidence that such models lead to a modest yet signicant improvement.

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