Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation

Thomas Brouwer, Jes Frellsen, Pietro Liò

Research output: Conference Article in Proceeding or Book/Report chapterArticle in proceedingsResearchpeer-review


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. Code and data related to this chapter are availabe at:
Original languageEnglish
Title of host publicationThe European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Database 2017
Publication date2017
ISBN (Print)Print ISBN 978-3-319-71248-2
ISBN (Electronic)978-3-319-71249-9
Publication statusPublished - 2017
SeriesLecture Notes in Computer Science


  • Bayesian Matrix Factorisation
  • Nonnegative Matrix Factorisation
  • Inference Approaches
  • Variational Bayesian Inference
  • Automatic Relevance Determination


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