Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorization

TL;DR

This paper establishes an upper bound on the Bayesian generalization error for non-negative matrix factorization, demonstrating improved error bounds compared to regular models through Bayesian learning.

Contribution

It introduces a theoretical analysis of NMF's generalization error using the real log canonical threshold, providing the first known upper bound in Bayesian learning context.

Findings

Bayesian learning reduces NMF's generalization error.

Theoretical upper bound on NMF's generalization error is derived.

NMF's error can be smaller than regular models when Bayesian methods are used.

Abstract

Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization method of NMF has not yet established. In this paper, we study the real log canonical threshold of NMF and give an upper bound of the generalization error in Bayesian learning. The results show that the generalization error of the matrix factorization can be made smaller than regular statistical models if Bayesian learning is applied.