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 posteriormean 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.
Original language | English (US) |
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Pages (from-to) | 501-508 |
Number of pages | 8 |
Journal | Journal of Machine Learning Research |
Volume | 9 |
State | Published - 2010 |
Event | 13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010 - Sardinia, Italy Duration: May 13 2010 → May 15 2010 |
Keywords
- Dirichlet process
- Factor models
- Grassman manifold
- Inverse regression
- Supervised dimension reduction
ASJC Scopus subject areas
- Control and Systems Engineering
- Software
- Statistics and Probability
- Artificial Intelligence