Partial Gaussian Graphical Model Estimation

TL;DR

This paper introduces a convex $ ext{l}_1$-regularized maximum-likelihood approach for estimating Gaussian graphical models from high-dimensional data, with proven statistical guarantees and competitive empirical results.

Contribution

It presents a novel convex formulation and an efficient block coordinate descent algorithm for partial Gaussian graphical model estimation, with theoretical and empirical validation.

Findings

Method achieves accurate estimation in high-dimensional settings.

Algorithm demonstrates competitive performance on synthetic and real data.

Statistical guarantees support the method's reliability.

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 $\ell_1$-regularized maximum-likelihood estimation, which can be solved via a block coordinate descent algorithm. Statistical estimation performance can be established for our method. The proposed approach has competitive empirical performance compared to existing methods, as demonstrated by various experiments on synthetic and real datasets.