Comparative Study of Inference Methods for Bayesian Nonnegative Matrix Factorisation
This work addresses the selection of inference methods for researchers and practitioners using Bayesian nonnegative matrix factorisation, but it is incremental as it primarily compares existing techniques with a new application.
The paper tackled the problem of comparing inference methods for Bayesian nonnegative matrix factorisation and tri-factorisation, finding that the variational Bayesian approach, which is new for these models, was evaluated alongside others for convergence, robustness to noise and sparsity, and efficiency with automatic model selection on synthetic and real-world datasets.
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.