An Improved Iterative Proportional Scaling Procedure for Gaussian Graphical Models

The maximum likelihood estimation of Gaussian graphical models is often carried out by the iterative proportional scaling (IPS) procedure. In this article, we propose an improvement to the IPS procedure by using local computation and by sharing computations on a junction tree T. The proposed procedure, called IIPS for short, adjusts node by node the marginals of the cliques of the underlying graph contained in the nodes of T, and sends messages between two adjacent nodes of T by an exchange operation for the propositional scaling step. We show, through complexity calculations and empirical examples, that the proposed TIPS procedure works more efficiently than the conventional IPS procedure for large Gaussian graphical models. Computer codes used in this article are available as an online supplement.