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2008 JMLR JMLR 2008

Consistency of Trace Norm Minimization

Abstract

Regularization by the sum of singular values, also referred to as the trace norm, is a popular technique for estimating low rank rectangular matrices. In this paper, we extend some of the consistency results of the Lasso to provide necessary and sufficient conditions for rank consistency of trace norm minimization with the square loss. We also provide an adaptive version that is rank consistent even when the necessary condition for the non adaptive version is not fulfilled. [abs] [ pdf ][ bib ] © JMLR 2008. (edit, beta)

🧭 Keyword Pioneer — low rank matrix
🐣 Hot Topic Early Bird — matrix factorization
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Security & Privacy, Speech & Audio

Authors

Francis R. Bach

Topics

Machine Learning > Core Methods > Regression Machine Learning > Optimization & Theory > Optimization Machine Learning > Optimization & Theory > Theory

Keywords

matrix factorization matrix completion low rank matrix trace norm rank consistency trace norm minimization
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