Online matrix prediction for sparse loss matrices

Ken Ichiro Moridomi, Kohei Hatano, Eiji Takimoto, Koji Tsuda

Research output: Contribution to journalConference articlepeer-review


We consider an online matrix prediction problem. FTRL is a standard method to deal with online prediction tasks, which makes predictions by minimizing the cumulative loss function and the regularizer function. There are three popular regularizer functions for matrices, Frobenius norm, negative entropy and log-determinant. We propose an FTRL based algorithm with log-determinant as the regularizer and show a regret bound of the algorithm. Our main contribution is to show that the log-determinant regularization is effective when loss matrices are sparse. We also show that our algorithm is optimal for the online collaborative filtering problem with the log-determinant regularization.

Original languageEnglish
Pages (from-to)250-265
Number of pages16
JournalJournal of Machine Learning Research
Issue number2014
Publication statusPublished - 2014
Event6th Asian Conference on Machine Learning, ACML 2014 - Nha Trang, Viet Nam
Duration: Nov 26 2014Nov 28 2014

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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