Name
Title | ||
|---|---|---|
Global Solution of Fully-Observed Variational Bayesian Matrix Factorization is Column-Wise Independent. |
Abstract | ||
|---|---|---|
Variational Bayesian matrix factorization (VBMF) efficiently approximates the posterior distribution of factorized matrices by assuming matrix-wise independence of the two factors. A recent study on fully-observed VBMF showed that, under a stronger assumption that the two factorized matrices are column-wise independent, the global optimal solution can be analytically computed. However, it was not clear how restrictive the column-wise independence assumption is. In this paper, we prove that the global solution under matrix-wise independence is actually column-wise independent, implying that the column-wise independence assumption is harmless. A practical consequence of our theoretical finding is that the global solution under matrix-wise independence (which is a standard setup) can be obtained analytically in a computationally very efficient way without any iterative algorithms. We experimentally illustrate advantages of using our analytic solution in probabilistic principal component analysis. |
Year | Venue | Keywords |
|---|---|---|
2011 | NIPS | matrix factorization |
Field | DocType | Citations |
Mathematical optimization,Matrix (mathematics),Matrix decomposition,Posterior probability,Probabilistic principal component analysis,Analytic solution,Statistical assumption,Mathematics,Bayesian probability | Conference | 5 |
PageRank | References | Authors |
0.53 | 8 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nakajima, Shinichi | 1 | 627 | 38.83 |
| Masashi Sugiyama | 2 | 3353 | 264.24 |
| S. Derin Babacan | 3 | 534 | 26.60 |