An Improved IPSP Procedure Via Junction Tree For Gaussian Graphical Models

Gaussian graphical models play a very important rolein solving high dimensional complex problems in statistics, where the most important problem is to solve the maximum likelihood estimation effectively. To solve this problem, we can use the IlPSalgorithm proposed by Xu et al. (2011), or the IPSP algorithm described by Xu et al. (2015). The IPSP procedure decomposes the global problem into several sub-problems on each group of the partition of cliques. The IPSP algorithm reduces the complexity of the IPS procedure. However, the complexity of the IPSP algorithm is still high, especially when the number of variables is large, In this paper, we use the IIPS algorithm to solve the sub-problems on each group of the partition of cliques. This will reduce the time complexity of the IPSP algorithm. We first describe a new definition of m-decomposition; and study its corresponding properties and the relationships between G and G*;and we apply the MCS-M algorithm to construct a clique tree used by the IIPS algorithm. Through simulation experiments, we find that the new method greatly reduces the complexity of the IPSP algorithm, and speeds up the computations.