B0575
Title: On sufficient graphical models
Authors: Kyongwon Kim - Ewha Womans University (Korea, South) [presenting]
Abstract: A sufficient graphical model is introduced by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in nature, as it does not make distributional assumptions such as the Gaussian or copula Gaussian assumptions. However, unlike a fully nonparametric graphical model, which relies on the high-dimensional kernel to characterize conditional independence, the graphical model is based on conditional independence given a set of sufficient predictors with a substantially reduced dimension. In this way, the curse of dimensionality is avoided that comes with a high-dimensional kernel. The population-level properties are developed, convergence rate, and variable selection consistency of the estimate. By simulation comparisons and an analysis of the DREAM 4 Challenge data set, it is demonstrated that the method outperforms the existing methods when the Gaussian or copula Gaussian assumptions are violated, and its performance remains excellent in the high-dimensional setting.
