High-Dimensional Bayesian Structure Learning in Gaussian Graphical Models using Marginal Pseudo-Likelihood

Gaussian graphical models depict the conditional dependencies between variables within a multivariate normal distribution in a graphical format. The identification of these graph structures is an area known as structure learning. However, when utilizing Bayesian methodologies in structure learning, computational complexities can arise, especially with high-dimensional graphs surpassing 250 nodes. This paper introduces two innovative search algorithms that employ marginal pseudo-likelihood to address this computational challenge. These methods can swiftly generate reliable estimations for problems encompassing 1000 variables in just a few minutes on standard computers. For those interested in practical applications, the code supporting this new approach is made available through the R package BDgraph.