Supervised Dimension Reduction Using Bayesian Mixture Modeling

Kai Mao, Feng Liang, Sayan Mukherjee
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:501-508, 2010.

Abstract

We develop a Bayesian framework for supervised dimension reduction using a flexible nonparametric Bayesian mixture modeling approach. Our method retrieves the dimension reduction or d.r. subspace by utilizing a dependent Dirichlet process that allows for natural clustering for the data in terms of both the response and predictor variables. Formal probabilistic models with likelihoods and priors are given and efficient posterior sampling of the d.r. subspace can be obtained by a Gibbs sampler. As the posterior draws are linear subspaces which are points on a Grassmann manifold, we output the posterior mean d.r. subspace with respect to geodesics on the Grassmannian. The utility of our approach is illustrated on a set of simulated and real examples. Some Key Words: supervised dimension reduction, inverse regression, Dirichlet process, factor models, Grassman manifold.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-mao10a, title = {Supervised Dimension Reduction Using Bayesian Mixture Modeling}, author = {Mao, Kai and Liang, Feng and Mukherjee, Sayan}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {501--508}, 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/mao10a/mao10a.pdf}, url = {https://proceedings.mlr.press/v9/mao10a.html}, abstract = {We develop a Bayesian framework for supervised dimension reduction using a flexible nonparametric Bayesian mixture modeling approach. Our method retrieves the dimension reduction or d.r. subspace by utilizing a dependent Dirichlet process that allows for natural clustering for the data in terms of both the response and predictor variables. Formal probabilistic models with likelihoods and priors are given and efficient posterior sampling of the d.r. subspace can be obtained by a Gibbs sampler. As the posterior draws are linear subspaces which are points on a Grassmann manifold, we output the posterior mean d.r. subspace with respect to geodesics on the Grassmannian. The utility of our approach is illustrated on a set of simulated and real examples. Some Key Words: supervised dimension reduction, inverse regression, Dirichlet process, factor models, Grassman manifold.} }
Endnote
%0 Conference Paper %T Supervised Dimension Reduction Using Bayesian Mixture Modeling %A Kai Mao %A Feng Liang %A Sayan Mukherjee %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-mao10a %I PMLR %P 501--508 %U https://proceedings.mlr.press/v9/mao10a.html %V 9 %X We develop a Bayesian framework for supervised dimension reduction using a flexible nonparametric Bayesian mixture modeling approach. Our method retrieves the dimension reduction or d.r. subspace by utilizing a dependent Dirichlet process that allows for natural clustering for the data in terms of both the response and predictor variables. Formal probabilistic models with likelihoods and priors are given and efficient posterior sampling of the d.r. subspace can be obtained by a Gibbs sampler. As the posterior draws are linear subspaces which are points on a Grassmann manifold, we output the posterior mean d.r. subspace with respect to geodesics on the Grassmannian. The utility of our approach is illustrated on a set of simulated and real examples. Some Key Words: supervised dimension reduction, inverse regression, Dirichlet process, factor models, Grassman manifold.
RIS
TY - CPAPER TI - Supervised Dimension Reduction Using Bayesian Mixture Modeling AU - Kai Mao AU - Feng Liang AU - Sayan Mukherjee 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-mao10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 501 EP - 508 L1 - http://proceedings.mlr.press/v9/mao10a/mao10a.pdf UR - https://proceedings.mlr.press/v9/mao10a.html AB - We develop a Bayesian framework for supervised dimension reduction using a flexible nonparametric Bayesian mixture modeling approach. Our method retrieves the dimension reduction or d.r. subspace by utilizing a dependent Dirichlet process that allows for natural clustering for the data in terms of both the response and predictor variables. Formal probabilistic models with likelihoods and priors are given and efficient posterior sampling of the d.r. subspace can be obtained by a Gibbs sampler. As the posterior draws are linear subspaces which are points on a Grassmann manifold, we output the posterior mean d.r. subspace with respect to geodesics on the Grassmannian. The utility of our approach is illustrated on a set of simulated and real examples. Some Key Words: supervised dimension reduction, inverse regression, Dirichlet process, factor models, Grassman manifold. ER -
APA
Mao, K., Liang, F. & Mukherjee, S.. (2010). Supervised Dimension Reduction Using Bayesian Mixture Modeling. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:501-508 Available from https://proceedings.mlr.press/v9/mao10a.html.

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