Statistics and Data Science Seminar
Sayan Mukherjee
Duke University
A Tale of Two Manifolds
Abstract: The focus is on the problem of supervised dimension reduction (SDR). We
first formulate the problem with respect to the inference of a geometric
property of the data, the gradient of the regression function with respect
to the manifold that supports the marginal distribution. We provide an
estimation algorithm, prove consistency, and explain why the gradient is
salient for dimension reduction. We then reformulate SDR in a
probabilistic framework and propose a Bayesian model, a mixture of inverse
regressions. In this modeling framework the Grassman manifold plays a
prominent role.
Wednesday September 15, 2010 at 3:00 PM in SEO 636