Bayesian Inference for Nonnegative Matrix Factorisation Models

By Ali Taylan Cemgil. Computational Intelligence and Neuroscience, 2009

436 citations recorded by the source corpus.

We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximum likelihood parameter estimation is carried out via the Expectation-Maximisation (EM) algorithm. Starting from this view, we develop full Bayesian inference via variational Bayes or Monte Carlo. Our construction retains conjugacy and enables us to develop more powerful models while retaining attractive features of standard NMF such as monotonic convergence and easy implementation. We illustrate our approach on model order selection and image reconstruction.

Subfields: Artificial Intelligence, Signal Processing

View Paper: https://www.semanticscholar.org/paper/341c82e2aff1cec82e81efed95aa0b9d1f699f52

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Citations in the corpus

A General Flexible Framework for the Handling of Prior Information in Audio Source Separation (2012, background): “There are also many works on NMF and its extensions [31,32,33,34,35,36] and on GMMs / HMMs [37,38] based on nongaussian models of the complex-valued STFT coe cients.”
A review on machine learning principles for multi-view biological data integration (2016, background): “Missing values can be nicely handled by weighted matrix factorizations [101] and Bayesian matrix factorizations [136, 137], which can ignore missing entries in their learning.”
Algorithms for Nonnegative Matrix Factorization with the β-Divergence (2010, methodology): “For β 6∈ {0, 1}, a suitable Bregman generating function is φ(y) = yβ/(β(β − 1)), as noted by Févotte and Cemgil (2009).”
Scalable Recommendation with Hierarchical Poisson Factorization (2015, methodology): “(See [20, 5].)”
Bayesian reasoning and machine learning (2012, neutral): “A fully probabilistic interpretation of PLSA can be made via Poisson processes[56].”
Scalable Recommendation with Poisson Factorization (2013, methodology): “) Independently of GaP, Bayesian Poisson factorization has been studied in the signal processing community for performing source separation from spectrogram data [6, 14].”
Reweighted Data for Robust Probabilistic Models (2016, background): “Poisson factorization ( PF ) offers a ﬂexible solution (Cemgil, 2009).”