|Interaction Detection for Index Models in High Dimension|
|Time：||Every Tuesday 10:10-12:00|
|Instructor：||Jun liu [Harvard University]|
|Place：||Conference Room 1, Jin Chun Yuan West Building|
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 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. The performance of the proposed procedure in comparison with some existing method is demonstrated through simulation studies.
Based on the joint work with Tingting Zhang, Wenxuan Zhong, Michael Zhu, and Bo Jiang.