Sayan Mukherjee : A Tale of Two Manifolds

Posted by , part of the Statistics and Data Science Seminar.

At

Sept. 15, 2010, 3 p.m.

In

SEO 636

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.