# Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation

arXiv: https://arxiv.org/abs/1707.05147 · HTML: https://mlsanity.com/paper/1707.05147/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2017.

## Built on by (most cited first, 1 of 1)

- [Entropy Minimizing Matrix Factorization](https://mlsanity.com/paper/2103.13487/) (2021)

## Abstract (arXiv)

In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synthetic and real-world datasets. Furthermore, we extend the models with the Bayesian automatic relevance determination prior, allowing the models to perform automatic model selection, and demonstrate its efficiency.