Non-parametric Bayesian simultaneous dimension reduction and regression on manifolds

K. Mao, Q. Wu, F. Liang, S. Mukherjee

Duke University and University of Illinois Urbana-Champaign

August 2008

We formulate a Bayesian non-parametric model for simultaneous dimension reduction and regression as well as inference of graphical models. The proposed model holds for both the classical setting of Euclidean subspaces and the Riemannian setting where the marginal distribution is concentrated on a manifold. The method is designed for the high-dimensional setting where the number of variables far exceed the number of observations. A Markov chain Monte Carlo procedure for inference of model parameters is provided. Properties of the method and its utility are elucidated using simulations and real data.

Keywords: Dimension reduction, Bayesian inference, graphical models, manifolds

The manuscript is available PDF format.