Collaborative filtering with the trace norm: Learning, bounding, and transducing

Ohad Shamir, Shai Shalev-Shwartz

Research output: Contribution to journalConference articlepeer-review

16 Scopus citations


Trace-norm regularization is a widely-used and successful approach for collaborative filtering and matrix completion. However, its theoretical understanding is surprisingly weak, and despite previous attempts, there are no distribution-free, non-trivial learning guarantees currently known. In this paper, we bridge this gap by providing such guarantees, under mild assumptions which correspond to collaborative filtering as performed in practice. In fact, we claim that previous difficulties partially stemmed from a mismatch between the standard learning-theoretic modeling of collaborative filtering, and its practical application. Our results also shed some light on the issue of collaborative filtering 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 significant improvement.

Original languageEnglish
Pages (from-to)661-678
Number of pages18
JournalProceedings of Machine Learning Research
StatePublished - 2011
Event24th International Conference on Learning Theory, COLT 2011 - Budapest, Hungary
Duration: 9 Jul 201111 Jul 2011


  • Collaborative filtering
  • Sample complexity
  • Trace-Norm regularization
  • Transductive learning


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