Journal article

Global Analytic Solution for Variational Bayesian Matrix Factorization

Nakajima S, Sugiyama M, Tomioka R ...see all

Advances in Neural Information Processing Systems 23 (Proceedings of NIPS) (2010) pp. 1-9

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Abstract

Bayesian methods of matrix factorization (MF) have been actively explored recently as promising alternatives to classical singular value decomposition. In this paper, we show that, despite the fact that the optimization problem is non-convex, the global optimal solution of variational Bayesian (VB) MF can be computed analytically by solving a quartic equation. This is highly advantageous over a popular VBMF algorithm based on iterated conditional modes since it can only find a local optimal solution after iterations. We further show that the global optimal solution of empirical VBMF (hyperparameters are also learned from data) can also be analytically computed. We illustrate the usefulness of our results through experiments.

Author-supplied keywords

  • matrix factorization
  • variational Bayes
  • variational inference

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Authors

  • Shinichi Nakajima

  • Masashi Sugiyama

  • Ryota Tomioka

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