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

arXiv: https://arxiv.org/abs/1612.04112 · HTML: https://mlsanity.com/paper/1612.04112/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2016.

## Built on by (most cited first, 10 of 10)

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- [Upper Bound of Real Log Canonical Threshold of Tensor Decomposition and its Application to Bayesian Inference](https://mlsanity.com/paper/2303.05731/) (2023)
- [An Asymptotic Equation Linking WAIC and WBIC in Singular Models](https://mlsanity.com/paper/2505.13902/) (2025)
- [Singularities of Non-negative Matrix Factorization and their application to Bayesian inference](https://mlsanity.com/paper/2609.34043/) (2026)

## Abstract (arXiv)

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.