Bayesian Inference in Sparse Gaussian Graphical Models
This work addresses the challenge of efficient and accurate sparse structure inference in probabilistic graphical models, with applications in fields like finance, though it is incremental in nature.
The paper tackles the problem of inferring sparse structures in Gaussian graphical models by introducing two new Bayesian inference methods, which achieve significant computational gains in high dimensions and outperform the graphical LASSO under similar computing costs.
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bayesian inference of sparse structures of Gaussian graphical models (GGMs). One is based on a simple modification of the cutting-edge block Gibbs sampler for sparse GGMs, which results in significant computational gains in high dimensions. The other method is based on a specific construction of the Hamiltonian Monte Carlo sampler, which results in further significant improvements. We compare our fully Bayesian approaches with the popular regularisation-based graphical LASSO, and demonstrate significant advantages of the Bayesian treatment under the same computing costs. We apply the methods to a broad range of simulated data sets, and a real-life financial data set.