Bayesian Generalized Kernel Models

Zhihua Zhang, Guang Dai, Donghui Wang, Michael I. Jordan
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:972-979, 2010.

Abstract

We propose a fully Bayesian approach for generalized kernel models (GKMs), which are extensions of generalized linear models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of GKMs. This mixture prior allows a fraction of the regression vector to be zero. Thus, it serves for sparse modeling and Bayesian computation. For inference, we exploit data augmentation methodology to develop a Markov chain Monte Carlo (MCMC) algorithm in which the reversible jump method is used for model selection and a Bayesian model averaging method is used for posterior prediction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-zhang10d, title = {Bayesian Generalized Kernel Models}, author = {Zhang, Zhihua and Dai, Guang and Wang, Donghui and Jordan, Michael I.}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {972--979}, 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/zhang10d/zhang10d.pdf}, url = {https://proceedings.mlr.press/v9/zhang10d.html}, abstract = {We propose a fully Bayesian approach for generalized kernel models (GKMs), which are extensions of generalized linear models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of GKMs. This mixture prior allows a fraction of the regression vector to be zero. Thus, it serves for sparse modeling and Bayesian computation. For inference, we exploit data augmentation methodology to develop a Markov chain Monte Carlo (MCMC) algorithm in which the reversible jump method is used for model selection and a Bayesian model averaging method is used for posterior prediction.} }
Endnote
%0 Conference Paper %T Bayesian Generalized Kernel Models %A Zhihua Zhang %A Guang Dai %A Donghui Wang %A Michael I. Jordan %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-zhang10d %I PMLR %P 972--979 %U https://proceedings.mlr.press/v9/zhang10d.html %V 9 %X We propose a fully Bayesian approach for generalized kernel models (GKMs), which are extensions of generalized linear models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of GKMs. This mixture prior allows a fraction of the regression vector to be zero. Thus, it serves for sparse modeling and Bayesian computation. For inference, we exploit data augmentation methodology to develop a Markov chain Monte Carlo (MCMC) algorithm in which the reversible jump method is used for model selection and a Bayesian model averaging method is used for posterior prediction.
RIS
TY - CPAPER TI - Bayesian Generalized Kernel Models AU - Zhihua Zhang AU - Guang Dai AU - Donghui Wang AU - Michael I. Jordan 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-zhang10d PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 972 EP - 979 L1 - http://proceedings.mlr.press/v9/zhang10d/zhang10d.pdf UR - https://proceedings.mlr.press/v9/zhang10d.html AB - We propose a fully Bayesian approach for generalized kernel models (GKMs), which are extensions of generalized linear models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of GKMs. This mixture prior allows a fraction of the regression vector to be zero. Thus, it serves for sparse modeling and Bayesian computation. For inference, we exploit data augmentation methodology to develop a Markov chain Monte Carlo (MCMC) algorithm in which the reversible jump method is used for model selection and a Bayesian model averaging method is used for posterior prediction. ER -
APA
Zhang, Z., Dai, G., Wang, D. & Jordan, M.I.. (2010). Bayesian Generalized Kernel Models. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:972-979 Available from https://proceedings.mlr.press/v9/zhang10d.html.

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