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JUN LIU - Harvard University

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” A Bayesian View of Sliced Inverse Regression with Interaction Detection”
21 September 2012 from 3:30 PM to 4:30 PM
201 Thomas Bldg.
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Previously we have proposed a Bayesian partition model for detecting
interactive variables in a classification setting with discrete
covariates. This framework takes advantage of the structure of the
naïve Bayes classifier and introduces latent indicator variables for
selecting variables and interactions. In our effort to extend the
methods to continuous covariates, we found interesting connections
with semi-parametric index models and the Sliced Inverse Regression
(SIR) method. In index models, the response is influenced by the
covariates through an unknown function of several linear combinations
of the predictors. Our finding of the Bayesian formulation of such
models enabled us to propose a set of new models and methods that can
effectively discover second-order effects and interactions among the
covariates. A two-stage stepwise procedure based on likelihood ratio
test is developed to select relevant predictors and a Bayesian model
with dynamic slicing scheme is derived. A full Bayesian analogy of SIR
is described. The performance of the proposed procedure in comparison
with some existing method is demonstrated through simulation studies.

This is based on the joint work with Bo Jiang, Wenxuan Zhong, Tingting
Zhang, Michael Zhu.

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