Dependent Indian Buffet Processes

Sinead Williamson, Peter Orbanz, Zoubin Ghahramani
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:924-931, 2010.

Abstract

Latent variable models represent hidden structure in observational data.To account for the distribution of the observational data changing over time, space or some other covariate, we need generalizations of latent variable models that explicitly capture this dependency on the covariate. A variety of such generalizations has been proposed for latent variable models based on the Dirichlet process. We address dependency on covariates in binary latent feature models, by introducing a dependent Indian buffet process. The model generates, for each value of the covariate, a binary random matrix with an unbounded number of columns. Evolution of the binary matrices over the covariate set is controlled by a hierarchical Gaussian process model. The choice of covariance functions controls the dependence structure and exchangeability properties of the model. We derive a Markov Chain Monte Carlo sampling algorithm for Bayesian inference, and provide experiments on both synthetic and real-world data. The experimental results show that explicit modeling of dependencies significantly improves accuracy of predictions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-williamson10a, title = {Dependent Indian Buffet Processes}, author = {Williamson, Sinead and Orbanz, Peter and Ghahramani, Zoubin}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {924--931}, 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/williamson10a/williamson10a.pdf}, url = {https://proceedings.mlr.press/v9/williamson10a.html}, abstract = {Latent variable models represent hidden structure in observational data.To account for the distribution of the observational data changing over time, space or some other covariate, we need generalizations of latent variable models that explicitly capture this dependency on the covariate. A variety of such generalizations has been proposed for latent variable models based on the Dirichlet process. We address dependency on covariates in binary latent feature models, by introducing a dependent Indian buffet process. The model generates, for each value of the covariate, a binary random matrix with an unbounded number of columns. Evolution of the binary matrices over the covariate set is controlled by a hierarchical Gaussian process model. The choice of covariance functions controls the dependence structure and exchangeability properties of the model. We derive a Markov Chain Monte Carlo sampling algorithm for Bayesian inference, and provide experiments on both synthetic and real-world data. The experimental results show that explicit modeling of dependencies significantly improves accuracy of predictions.} }
Endnote
%0 Conference Paper %T Dependent Indian Buffet Processes %A Sinead Williamson %A Peter Orbanz %A Zoubin Ghahramani %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-williamson10a %I PMLR %P 924--931 %U https://proceedings.mlr.press/v9/williamson10a.html %V 9 %X Latent variable models represent hidden structure in observational data.To account for the distribution of the observational data changing over time, space or some other covariate, we need generalizations of latent variable models that explicitly capture this dependency on the covariate. A variety of such generalizations has been proposed for latent variable models based on the Dirichlet process. We address dependency on covariates in binary latent feature models, by introducing a dependent Indian buffet process. The model generates, for each value of the covariate, a binary random matrix with an unbounded number of columns. Evolution of the binary matrices over the covariate set is controlled by a hierarchical Gaussian process model. The choice of covariance functions controls the dependence structure and exchangeability properties of the model. We derive a Markov Chain Monte Carlo sampling algorithm for Bayesian inference, and provide experiments on both synthetic and real-world data. The experimental results show that explicit modeling of dependencies significantly improves accuracy of predictions.
RIS
TY - CPAPER TI - Dependent Indian Buffet Processes AU - Sinead Williamson AU - Peter Orbanz AU - Zoubin Ghahramani 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-williamson10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 924 EP - 931 L1 - http://proceedings.mlr.press/v9/williamson10a/williamson10a.pdf UR - https://proceedings.mlr.press/v9/williamson10a.html AB - Latent variable models represent hidden structure in observational data.To account for the distribution of the observational data changing over time, space or some other covariate, we need generalizations of latent variable models that explicitly capture this dependency on the covariate. A variety of such generalizations has been proposed for latent variable models based on the Dirichlet process. We address dependency on covariates in binary latent feature models, by introducing a dependent Indian buffet process. The model generates, for each value of the covariate, a binary random matrix with an unbounded number of columns. Evolution of the binary matrices over the covariate set is controlled by a hierarchical Gaussian process model. The choice of covariance functions controls the dependence structure and exchangeability properties of the model. We derive a Markov Chain Monte Carlo sampling algorithm for Bayesian inference, and provide experiments on both synthetic and real-world data. The experimental results show that explicit modeling of dependencies significantly improves accuracy of predictions. ER -
APA
Williamson, S., Orbanz, P. & Ghahramani, Z.. (2010). Dependent Indian Buffet Processes. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:924-931 Available from https://proceedings.mlr.press/v9/williamson10a.html.

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