Partial Gaussian Graphical Model Estimation

Xiao-Tong Yuan, Tong Zhang

Abstract: This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\ell_{1}$</tex></formula> -regularized maximum-likelihood estimation, which can be solved via a smoothing approximation algorithm. Statistical estimation performance can be established for our method. The proposed approach has competitive empirical performance compared with existing methods, as demonstrated by various experiments on synthetic and real data sets.