Sparse Median Graphs Estimation in a High Dimensional Semiparametric Model

Abstract

We propose a unified framework for conducting inference on complex aggregated data in high dimensional settings. We assume the data are a collection of multiple non- Gaussian realizations with underlying undirected graphical structures. Using the concept of median graphs in summarizing the commonality across these graphical structures, we provide a novel semiparametric approach to modeling such complex aggregated data, along with robust estimation of the median graph, which is assumed to be sparse. We prove the estimator is consistent in graph recovery and give an upper bound on the rate of convergence. We further provide thorough numerical analysis on both synthetic and real datasets to illustrate the empirical usefulness of the proposed models and methods.