Sparse Median Graphs Estimation in a High-Dimensional Semiparametric Model

• Activity Number: 224
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Fang Han*+ and Han Liu and Brian Scott Caffo
• Companies: Johns Hopkins University and Princeton University and Johns Hopkins University
• Keywords: median graph ; semiparametric statistics ; graphical model ; high dimensional statistics

Abstract

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Utilizing the concept of median graphs in summarizing the commonality across these graphical structures, a novel semiparametric approach to modeling such complex aggregated data is provided along with robust estimation of the median graph, which is assumed to be sparse. The estimator is proved to be consistent in graph recovery and an upper bound on the rate of convergence is given. Experiments on both synthetic and real datasets are conducted to illustrate the empirical usefulness of the proposed models and methods.