Reversible Jump MCMC for Non-Negative Matrix Factorization

Mingjun Zhong, Mark Girolami
Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, PMLR 5:663-670, 2009.

Abstract

We present a fully Bayesian approach to Non-Negative Matrix Factorisation (NMF) by developing a Reversible Jump Markov Chain Monte Carlo (RJMCMC) method which provides full posteriors over the matrix components. In addition the NMF model selection issue is addressed, for the first time, as our RJMCMC procedure provides the posterior distribution over the matrix dimensions and therefore the number of components in the NMF model. A comparative analysis is provided with the Bayesian Information Criterion (BIC) and model selection employing estimates of the marginal likelihood. An illustrative synthetic example is provided using blind mixtures of images. This is then followed by a large scale study of the recovery of component spectra from multiplexed Raman readouts. The power and flexibility of the Bayesian methodology and the proposed RJMCMC procedure to objectively assess differing model structures and infer the corresponding plausible component spectra for this complex data is demonstrated convincingly.

Cite this Paper

BibTeX
@InProceedings{pmlr-v5-zhong09a, title = {Reversible Jump MCMC for Non-Negative Matrix Factorization}, author = {Zhong, Mingjun and Girolami, Mark}, booktitle = {Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics}, pages = {663--670}, year = {2009}, editor = {van Dyk, David and Welling, Max}, volume = {5}, series = {Proceedings of Machine Learning Research}, address = {Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v5/zhong09a/zhong09a.pdf}, url = {https://proceedings.mlr.press/v5/zhong09a.html}, abstract = {We present a fully Bayesian approach to Non-Negative Matrix Factorisation (NMF) by developing a Reversible Jump Markov Chain Monte Carlo (RJMCMC) method which provides full posteriors over the matrix components. In addition the NMF model selection issue is addressed, for the first time, as our RJMCMC procedure provides the posterior distribution over the matrix dimensions and therefore the number of components in the NMF model. A comparative analysis is provided with the Bayesian Information Criterion (BIC) and model selection employing estimates of the marginal likelihood. An illustrative synthetic example is provided using blind mixtures of images. This is then followed by a large scale study of the recovery of component spectra from multiplexed Raman readouts. The power and flexibility of the Bayesian methodology and the proposed RJMCMC procedure to objectively assess differing model structures and infer the corresponding plausible component spectra for this complex data is demonstrated convincingly.} }
Endnote
%0 Conference Paper %T Reversible Jump MCMC for Non-Negative Matrix Factorization %A Mingjun Zhong %A Mark Girolami %B Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2009 %E David van Dyk %E Max Welling %F pmlr-v5-zhong09a %I PMLR %P 663--670 %U https://proceedings.mlr.press/v5/zhong09a.html %V 5 %X We present a fully Bayesian approach to Non-Negative Matrix Factorisation (NMF) by developing a Reversible Jump Markov Chain Monte Carlo (RJMCMC) method which provides full posteriors over the matrix components. In addition the NMF model selection issue is addressed, for the first time, as our RJMCMC procedure provides the posterior distribution over the matrix dimensions and therefore the number of components in the NMF model. A comparative analysis is provided with the Bayesian Information Criterion (BIC) and model selection employing estimates of the marginal likelihood. An illustrative synthetic example is provided using blind mixtures of images. This is then followed by a large scale study of the recovery of component spectra from multiplexed Raman readouts. The power and flexibility of the Bayesian methodology and the proposed RJMCMC procedure to objectively assess differing model structures and infer the corresponding plausible component spectra for this complex data is demonstrated convincingly.
RIS
TY - CPAPER TI - Reversible Jump MCMC for Non-Negative Matrix Factorization AU - Mingjun Zhong AU - Mark Girolami BT - Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics DA - 2009/04/15 ED - David van Dyk ED - Max Welling ID - pmlr-v5-zhong09a PB - PMLR DP - Proceedings of Machine Learning Research VL - 5 SP - 663 EP - 670 L1 - http://proceedings.mlr.press/v5/zhong09a/zhong09a.pdf UR - https://proceedings.mlr.press/v5/zhong09a.html AB - We present a fully Bayesian approach to Non-Negative Matrix Factorisation (NMF) by developing a Reversible Jump Markov Chain Monte Carlo (RJMCMC) method which provides full posteriors over the matrix components. In addition the NMF model selection issue is addressed, for the first time, as our RJMCMC procedure provides the posterior distribution over the matrix dimensions and therefore the number of components in the NMF model. A comparative analysis is provided with the Bayesian Information Criterion (BIC) and model selection employing estimates of the marginal likelihood. An illustrative synthetic example is provided using blind mixtures of images. This is then followed by a large scale study of the recovery of component spectra from multiplexed Raman readouts. The power and flexibility of the Bayesian methodology and the proposed RJMCMC procedure to objectively assess differing model structures and infer the corresponding plausible component spectra for this complex data is demonstrated convincingly. ER -
APA
Zhong, M. & Girolami, M.. (2009). Reversible Jump MCMC for Non-Negative Matrix Factorization. Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 5:663-670 Available from https://proceedings.mlr.press/v5/zhong09a.html.

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