Partial correlation graphical LASSO

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