A0414
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 that comes with a high-dimensional kernel is avoided. The population-level properties, convergence rate, and variable selection consistency of the estimate are developed. By simulation comparisons and an analysis of the DREAM 4 Challenge data set, the method is demonstrated to outperform the existing methods when the Gaussian or copula Gaussian assumptions are violated, and its performance remains excellent in the high-dimensional setting.
