Sparse Networks Through Regularised Regressions

Abstract

We propose a Bayesian approach to the problem of variable selection and shrinkage in high dimensional sparse regression models where the regularisation method is an extension of a previous LASSO. The model allows us to include a large number of institutions which improves the identification of the relationship and maintains at the same time the flexibility of the univariate framework. Furthermore, we obtain a weighted directed network since the adjacency matrix is built “row by row” using for each institutions the posterior inclusion probabilities of the other institutions in the system.