Inference on high-dimensional graphical models via pairwise likelihood truncation

Undirected graphical models are popular in a number of fields due to their interpretablity and flexibility in describing complex multivariate distributions. Efficient estimation and selection of graphs, however, remain challenging when the number of connections is large relative to the sample size, even under the Gaussian distributional assumption. Within a composite likelihood framework, a novel methodology which simultaneously estimates parameters and selects edges is proposed. The procedure consists of minimizing the divergence of the pairwise composite likelihood score from the full likelihood score, subject to a constraint representing the graph sparsity. The empirical performance of such approach is assessed through data simulated from a Gaussian random field.