Kai Mao, Qiang Wu, Feng Liang, Sayan Mukherjee

Duke University, Michigan State University, UIUC

May 2009

We study and develop two Bayesian frameworks for supervised dimension reduction that apply to nonlinear manifolds: Bayesian mixtures of inverse regressions and gradient based methods. Formal probabilistic models with likelihoods and priors are given for both methods and efficient posterior estimates of the effective dimension reduction space and predictive factors can be obtained by a Gibbs sampling procedure. In the case of the gradient based methods estimates of conditional dependence between covariates predictive of the response can also be inferred. Relations to manifold learning and Bayesian factor models are made explicit. The utility of the approach is illustrated on simulated and real examples.

Keywords: Supervised dimension reduction, Manifold learning, Inverse regression, Factor models, Graphical models

The manuscript is available PDF format (428kb).

Cite as:

@TechReport{Mao:Wu:Liang:Mukh:2009,
      Author = "Kai Mao, Qiang Wu, Feng Liang, Sayan Mukherjee",
       Title = "Two models for Bayesian supervised dimension reduction",
 Institution = "Duke University Department of Statistical Science",
        Type = "Discussion Paper",
      Number = "2009-08",
         URL = "http://ftp.stat.duke.edu/pub/WorkingPapers/09-08.html",
        Year = 2009,
}