Learning Gaussian Graphical Models Using Discriminated Hub Graphical Lasso
This work addresses a specific challenge in statistical learning for researchers in fields like bioinformatics, but it is incremental as it builds directly on existing Hub Graphical Lasso methods.
The paper tackled the problem of estimating precision matrices in Gaussian graphical models by developing Discriminated Hub Graphical Lasso (DHGL), which incorporates prior hub information to improve upon Hub Graphical Lasso (HGL), resulting in better estimation when hubs are known and robust performance even with incorrect prior information.
We develop a new method called Discriminated Hub Graphical Lasso (DHGL) based on Hub Graphical Lasso (HGL) by providing prior information of hubs. We apply this new method in two situations: with known hubs and without known hubs. Then we compare DHGL with HGL using several measures of performance. When some hubs are known, we can always estimate the precision matrix better via DHGL than HGL. When no hubs are known, we use Graphical Lasso (GL) to provide information of hubs and find that the performance of DHGL will always be better than HGL if correct prior information is given and will seldom degenerate when the prior information is wrong.