Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study

Abstract

The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the different type of priors considered on matrices to favour low-rank. We also prove that the obtained Bayesian estimators, under suitable assumptions, enjoys the same optimality properties as the ones based on penalization.

Cite

Text

Alquier. "Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study." International Conference on Algorithmic Learning Theory, 2013. doi:10.1007/978-3-642-40935-6_22

Markdown

[Alquier. "Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study." International Conference on Algorithmic Learning Theory, 2013.](https://mlanthology.org/alt/2013/alquier2013alt-bayesian/) doi:10.1007/978-3-642-40935-6_22

BibTeX

@inproceedings{alquier2013alt-bayesian,
  title     = {{Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study}},
  author    = {Alquier, Pierre},
  booktitle = {International Conference on Algorithmic Learning Theory},
  year      = {2013},
  pages     = {309-323},
  doi       = {10.1007/978-3-642-40935-6_22},
  url       = {https://mlanthology.org/alt/2013/alquier2013alt-bayesian/}
}