|
Abstract
|
The regression problem can be approached from an inverse perspective, generally formulated as index models, in which the response variable is influenced by covariates through an unknown function of several linear combinations of the predictors. We found an interesting Bayesian formulation of such models, which enables us to propose a set of efficient test statistics that can be used to discover second-order effects and multi-way interactions among thousands of candidate predictors in linear time. 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 connection of dynamic slicing with some recent advances in information theory is uncovered and discussed. The performance of the proposed procedure in comparison with some existing method is demonstrated through simulation studies.
|
