Nonparametric Bayesian Matrix Factorization by Power-EP

Nan Ding, Yuan Qi, Rongjing Xiang, Ian Molloy, Ninghui Li
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:169-176, 2010.

Abstract

Many real-world applications can be modeled by matrix factorization. By approximating an observed data matrix as the product of two latent matrices, matrix factorization can reveal hidden structures embedded in data. A common challenge to use matrix factorization is determining the dimensionality of the latent matrices from data. Indian Buffet Processes (IBPs) enable us to apply the nonparametric Bayesian machinery to address this challenge. However, it remains a difficult task to learn nonparametric Bayesian matrix factorization models. In this paper, we propose a novel variational Bayesian method based on new equivalence classes of infinite matrices for learning these models. Furthermore, inspired by the success of nonnegative matrix factorization on many learning problems, we impose nonnegativity constraints on the latent matrices and mix variational inference with expectation propagation. This mixed inference method is unified in a power expectation propagation framework. Experimental results on image decomposition demonstrate the superior computational efficiency and the higher prediction accuracy of our methods compared to alternative Monte Carlo and variational inference methods for IBP models. We also apply the new methods to collaborative filtering and role mining and show the improved predictive performance over other matrix factorization methods.

Cite this Paper


BibTeX
@InProceedings{pmlr-v9-ding10a, title = {Nonparametric Bayesian Matrix Factorization by Power-EP}, author = {Ding, Nan and Qi, Yuan and Xiang, Rongjing and Molloy, Ian and Li, Ninghui}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {169--176}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/ding10a/ding10a.pdf}, url = { http://proceedings.mlr.press/v9/ding10a.html }, abstract = {Many real-world applications can be modeled by matrix factorization. By approximating an observed data matrix as the product of two latent matrices, matrix factorization can reveal hidden structures embedded in data. A common challenge to use matrix factorization is determining the dimensionality of the latent matrices from data. Indian Buffet Processes (IBPs) enable us to apply the nonparametric Bayesian machinery to address this challenge. However, it remains a difficult task to learn nonparametric Bayesian matrix factorization models. In this paper, we propose a novel variational Bayesian method based on new equivalence classes of infinite matrices for learning these models. Furthermore, inspired by the success of nonnegative matrix factorization on many learning problems, we impose nonnegativity constraints on the latent matrices and mix variational inference with expectation propagation. This mixed inference method is unified in a power expectation propagation framework. Experimental results on image decomposition demonstrate the superior computational efficiency and the higher prediction accuracy of our methods compared to alternative Monte Carlo and variational inference methods for IBP models. We also apply the new methods to collaborative filtering and role mining and show the improved predictive performance over other matrix factorization methods.} }
Endnote
%0 Conference Paper %T Nonparametric Bayesian Matrix Factorization by Power-EP %A Nan Ding %A Yuan Qi %A Rongjing Xiang %A Ian Molloy %A Ninghui Li %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-ding10a %I PMLR %P 169--176 %U http://proceedings.mlr.press/v9/ding10a.html %V 9 %X Many real-world applications can be modeled by matrix factorization. By approximating an observed data matrix as the product of two latent matrices, matrix factorization can reveal hidden structures embedded in data. A common challenge to use matrix factorization is determining the dimensionality of the latent matrices from data. Indian Buffet Processes (IBPs) enable us to apply the nonparametric Bayesian machinery to address this challenge. However, it remains a difficult task to learn nonparametric Bayesian matrix factorization models. In this paper, we propose a novel variational Bayesian method based on new equivalence classes of infinite matrices for learning these models. Furthermore, inspired by the success of nonnegative matrix factorization on many learning problems, we impose nonnegativity constraints on the latent matrices and mix variational inference with expectation propagation. This mixed inference method is unified in a power expectation propagation framework. Experimental results on image decomposition demonstrate the superior computational efficiency and the higher prediction accuracy of our methods compared to alternative Monte Carlo and variational inference methods for IBP models. We also apply the new methods to collaborative filtering and role mining and show the improved predictive performance over other matrix factorization methods.
RIS
TY - CPAPER TI - Nonparametric Bayesian Matrix Factorization by Power-EP AU - Nan Ding AU - Yuan Qi AU - Rongjing Xiang AU - Ian Molloy AU - Ninghui Li BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-ding10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 169 EP - 176 L1 - http://proceedings.mlr.press/v9/ding10a/ding10a.pdf UR - http://proceedings.mlr.press/v9/ding10a.html AB - Many real-world applications can be modeled by matrix factorization. By approximating an observed data matrix as the product of two latent matrices, matrix factorization can reveal hidden structures embedded in data. A common challenge to use matrix factorization is determining the dimensionality of the latent matrices from data. Indian Buffet Processes (IBPs) enable us to apply the nonparametric Bayesian machinery to address this challenge. However, it remains a difficult task to learn nonparametric Bayesian matrix factorization models. In this paper, we propose a novel variational Bayesian method based on new equivalence classes of infinite matrices for learning these models. Furthermore, inspired by the success of nonnegative matrix factorization on many learning problems, we impose nonnegativity constraints on the latent matrices and mix variational inference with expectation propagation. This mixed inference method is unified in a power expectation propagation framework. Experimental results on image decomposition demonstrate the superior computational efficiency and the higher prediction accuracy of our methods compared to alternative Monte Carlo and variational inference methods for IBP models. We also apply the new methods to collaborative filtering and role mining and show the improved predictive performance over other matrix factorization methods. ER -
APA
Ding, N., Qi, Y., Xiang, R., Molloy, I. & Li, N.. (2010). Nonparametric Bayesian Matrix Factorization by Power-EP. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:169-176 Available from http://proceedings.mlr.press/v9/ding10a.html .

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