Joint estimation of multiple high-dimensional Gaussian copula graphical models

摘要

A joint estimation approach for multiple high-dimensional Gaussian copula graphical models is proposed, which achieves estimation robustness by exploiting non-parametric rank-based correlation coefficient estimators. Although we focus on continuous data in this paper, the proposed method can be extended to deal with binary or mixed data. Based on a weighted /1 minimisation problem, the estimators can be obtained by implementing second-order cone programming. Theoretical properties of the procedure are investigated. We show that the proposed joint estimation procedure leads to a faster convergence rate than estimating the graphs individually. It is also shown that the proposed procedure achieves an exact graph structure recovery with probability tending to 1 under certain regularity conditions. Besides theoretical analysis, we conduct numerical simulations to compare the estimation performance and graph recovery performance of some state-of-the-art methods including both joint estimation methods and estimation methods for individuals. The proposed method is then applied to a gene expression data set, which illustrates its practical usefulness.