Implicit Regularization in Variational Bayesian Matrix Factorization
Abstract
Matrix factorization into the product of low-rank matrices induces non-identifiability, i.e.,the mapping between the target matrix and factorized matrices is not one-to-one. In this paper, we theoretically investigate the influence of non-identifiability on Bayesian matrix factorization. More specifically, we show that a variational Bayesian method involves regularization effect even when the prior is non-informative, which is intrinsically different from the maximum a posteriori approach. We also extend our analysis to empirical Bayes scenarios where hyper parameters are also learned from data.
Cite
Text
Nakajima and Sugiyama. "Implicit Regularization in Variational Bayesian Matrix Factorization." International Conference on Machine Learning, 2010.Markdown
[Nakajima and Sugiyama. "Implicit Regularization in Variational Bayesian Matrix Factorization." International Conference on Machine Learning, 2010.](https://mlanthology.org/icml/2010/nakajima2010icml-implicit/)BibTeX
@inproceedings{nakajima2010icml-implicit,
title = {{Implicit Regularization in Variational Bayesian Matrix Factorization}},
author = {Nakajima, Shinichi and Sugiyama, Masashi},
booktitle = {International Conference on Machine Learning},
year = {2010},
pages = {815-822},
url = {https://mlanthology.org/icml/2010/nakajima2010icml-implicit/}
}