Penalized Maximum Likelihood Estimation of Multi-layered Gaussian Graphical Models

摘要

Analyzing multi-layered graphical models provides insight intounderstanding the conditional relationships among nodes withinlayers after adjusting for and quantifying the effects of nodesfrom other layers. We obtain the penalized maximum likelihoodestimator for Gaussian multi-layered graphical models, based ona computational approach involving screening of variables,iterative estimation of the directed edges between layers andundirected edges within layers and a final refitting andstability selection step that provides improved performance infinite sample settings. We establish the consistency of theestimator in a high-dimensional setting. To obtain this result,we develop a strategy that leverages the biconvexity of thelikelihood function to ensure convergence of the developediterative algorithm to a stationary point, as well as carefuluniform error control of the estimates over iterations. Theperformance of the maximum likelihood estimator is illustratedon synthetic data. color="gray">