Name
Abstract | ||
|---|---|---|
The variational Bayesian (VB) approximation is known to be a promising approach to Bayesian estimation, when the rigorous calculation of the Bayes posterior is intractable. The VB approximation has been successfully applied to matrix factorization (MF), offering automatic dimensionality selection for principal component analysis. Generally, finding the VB solution is a nonconvex problem, and most methods rely on a local search algorithm derived through a standard procedure for the VB approximation. In this paper, we show that a better option is available for fully-observed VBMF--the global solution can be analytically computed. More specifically, the global solution is a reweighted SVD of the observed matrix, and each weight can be obtained by solving a quartic equation with its coefficients being functions of the observed singular value. We further show that the global optimal solution of empirical VBMF (where hyperparameters are also learned from data) can also be analytically computed. We illustrate the usefulness of our results through experiments in multi-variate analysis. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.5555/2567709.2502582 | Journal of Machine Learning Research |
Keywords | Field | DocType |
observed matrix,vb solution,fully-observed vbmf,empirical vbmf,vb approximation,observed singular value,global solution,bayesian estimation,multi-variate analysis,global analytic solution,global optimal solution,matrix factorization | Applied mathematics,Singular value,Matrix (mathematics),Artificial intelligence,Bayes estimator,Bayes' theorem,Singular value decomposition,Mathematical optimization,Pattern recognition,Hyperparameter,Matrix decomposition,Local search (optimization),Mathematics | Journal |
Volume | Issue | ISSN |
14 | 1 | 1532-4435 |
Citations | PageRank | References |
20 | 0.75 | 21 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nakajima, Shinichi | 1 | 627 | 38.83 |
| Masashi Sugiyama | 2 | 3353 | 264.24 |
| S. Derin Babacan | 3 | 534 | 26.60 |
| Ryota Tomioka | 4 | 1367 | 91.68 |