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Global Analytic Solution for Variational Bayesian Matrix Factorization
Shinichi Nakajima · Masashi Sugiyama · Ryota Tomioka

Wed Dec 08 09:55 AM -- 10:00 AM (PST) @ Regency Ballroom

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 Information

Shinichi Nakajima (Technische Universität Berlin)
Masashi Sugiyama (RIKEN / University of Tokyo)
Ryota Tomioka (Microsoft Research Cambridge)

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