Partial Correlation Graphical LASSO

TL;DR

This paper introduces a scale-invariant penalty based on partial correlations for Gaussian graphical models, improving inference robustness and performance over traditional methods that depend on data standardization.

Contribution

It proposes the partial correlation graphical LASSO, a novel scale-invariant penalty method, and demonstrates its advantages through simulations and real data analysis.

Findings

Scale invariance improves inference robustness.

Partial correlation penalty enhances model accuracy.

Method shows practical benefits in real datasets.

Abstract

Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardises the observed data to unit sample variances. We show that such standardisation can have a strong effect on inference and introduce a new family of penalties based on partial correlations. We show that the latter, as well as the maximum likelihood, $L_0$ and logarithmic penalties are scale invariant. We illustrate the use of one such penalty, the partial correlation graphical LASSO, which sets an $L_{1}$ penalty on partial correlations. The associated optimization problem is no longer convex, but is conditionally convex. We show via simulated examples and in two real datasets that, besides being scale invariant, there can be important gains in terms of inference.