Generalized information criterion for model selection in penalized graphical models

TL;DR

This paper proposes an efficient estimator based on the generalized information criterion for model selection in penalized Gaussian copula graphical models, demonstrating improved support recovery over traditional criteria.

Contribution

It introduces a computationally feasible estimator for high-dimensional penalized graphical models, applicable to various penalties, and compares its performance with existing criteria.

Findings

Performs similarly to KL oracle estimator

Improves BIC support recovery

Outperforms AIC, BIC, and cross-validation in simulations

Abstract

This paper introduces an estimator of the relative directed distance between an estimated model and the true model, based on the Kulback-Leibler divergence and is motivated by the generalized information criterion proposed by Konishi and Kitagawa. This estimator can be used to select model in penalized Gaussian copula graphical models. The use of this estimator is not feasible for high-dimensional cases. However, we derive an efficient way to compute this estimator which is feasible for the latter class of problems. Moreover, this estimator is, generally, appropriate for several penalties such as lasso, adaptive lasso and smoothly clipped absolute deviation penalty. Simulations show that the method performs similarly to KL oracle estimator and it also improves BIC performance in terms of support recovery of the graph. Specifically, we compare our method with Akaike information criterion, Bayesian information criterion and cross validation for band, sparse and dense network structures.