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JMLR
2010

Supervised Dimension Reduction Using Bayesian Mixture Modeling

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Supervised Dimension Reduction Using Bayesian Mixture Modeling
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.
Kai Mao, Feng Liang, Sayan Mukherjee
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JMLR
Authors Kai Mao, Feng Liang, Sayan Mukherjee
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