A Min‐Max conditional covariance algorithm for structure learning of Gaussian graphical models

Abstract

The Gaussian graphical models provide a useful statistical framework for analyzing the linear dependence among continuous random variables. In this paper, we propose a learning algorithm to reconstruct the graph structure of the high‐dimensional Gaussian random vector from observation data. The algorithm is constituted by two conditional covariance threshold tests to identify the presence of the edges. We present a procedure called Min‐Max conditional covariance to estimate the test statistics and prove that the proposed algorithm has high computational efficiency and asymptotic consistency. The performance of the proposed methods is confirmed through numerical simulations on synthetic data and through a real‐world application to foreign exchange data.