Online Program Home
  My Program

All Times EDT

Abstract Details

Activity Number: 282 - Complex Functional Data Analysis with Biomedical Applications
Type: Invited
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
Sponsor: Section on Nonparametric Statistics
Abstract #309481
Title: On Sufficient Graphical Models
Author(s): Bing Li* and Kyongwon Kim
Companies: Pennsylvania State University and Pennsylvania State University
Keywords: Conjoined Conditional Covariance Operator; Generalized Sliced Inverse Regression; Nonlinear Sufficient Dimension Reduction; Reproducing Kernel Hilbert Space

We introduce a Sufficient Graphical Model 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, our graphical model is based on conditional independence given a set of sufficient predictors with a substantially reduced dimension. In this way we avoid the the curse of dimensionality that comes with a high-dimensional kernel. We develop the population-level properties, convergence rate, and variable selection consistency of our estimate. By simulation comparisons and an analysis of the DREAM 4 Challenge data set, we demonstrate that our method outperforms the existing methods when the Gaussian or copula Gaussian assumptions are violated, and its performance remains excellent in the high-dimensional setting.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2020 program