Joint estimation of multiple Gaussian graphical models across unbalanced classes

The problem of jointly estimating unbalanced multi-class Gaussian graphical models is considered. Most existing methods require equal or similar sample sizes among classes. However, many real applications do not have similar sample sizes. Hence, the joint adaptive graphical lasso, a weighted l1 penalized approach is proposed for unbalanced multi-class problems. The joint adaptive graphical lasso approach combines information across classes so that their common characteristics can be shared during the estimation process. Regularization is also introduced into the adaptive term. Simulation studies show that the new approach performs better than existing methods in terms of false positive rate, accuracy, Mathews correlation coefficient, and false discovery rate. The advantages of the new approach are also demonstrated using a liver cancer data set.