An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization
Machine Learning
2018-06-27 v4 Statistics Theory
Statistics Theory
Abstract
The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods non-negative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general class of prior distributions and shows how the prior affects the rate of convergence.
Cite
@article{arxiv.1601.01345,
title = {An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization},
author = {Pierre Alquier and Benjamin Guedj},
journal= {arXiv preprint arXiv:1601.01345},
year = {2018}
}
Comments
This is the corrected version of the published paper P. Alquier, B. Guedj, An Oracle Inequality for Quasi-Bayesian Non-negative Matrix Factorization, Mathematical Methods of Statistics, 2017, vol. 26, no. 1, pp. 55-67. Since then Arnak Dalalyan (ENSAE) found a mistake in the proofs. We fixed the mistake at the price of a slightly different logarithmic term in the bound