An alternative to joint graphical lasso for learning multiple Gaussian graphical models

Gaussian graphical models are widely used to learn the conditional independence structure of a set of random variables. This is done through the nonzero elements of its precision matrix. In many practical situations, one needs to estimate multiple graphical models due to a group structure of the data. We propose a neighbourhood approach to jointly learn multiple Gaussian graphical models. Our method estimates the edge set of each graph through joint lasso regression, and a constrained maximum likelihood method is then used to obtain precision matrices. The estimation procedure can be refined with prior information about relations among groups.