Fast Bayesian Non-Negative Matrix Factorisation and Tri-Factorisation
This work addresses a computational bottleneck for researchers and practitioners using matrix factorisation techniques in data analysis, though it appears incremental as it builds on existing variational Bayesian methods.
The authors tackled the problem of slow convergence in Bayesian non-negative matrix factorisation and tri-factorisation by developing a fast variational Bayesian algorithm. Their approach achieved faster convergence per iteration and wall-clock time than Gibbs sampling and non-probabilistic methods, without requiring additional samples for posterior estimation.
We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and non-probabilistic approaches, and do not require additional samples to estimate the posterior. We show that in particular for matrix tri-factorisation convergence is difficult, but our variational Bayesian approach offers a fast solution, allowing the tri-factorisation approach to be used more effectively.