On some algorithms for estimation in Gaussian graphical models

In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, resulting in increased speed when graphs are sparse and we compare this to an algorithm based on convex duality and operating on the covariance matrix by neighbourhood coordinate descent, essentially corresponding to the graphical lasso with zero penalty. For large, sparse graphs, this version of the iterative proportional scaling algorithm appears feasible and has simple convergence properties. The algorithm based on neighbourhood coordinate descent is extremely fast and less dependent on sparsity, but needs a positive definite starting value to converge, which may be difficult to achieve when the number of variables exceeds the number of observations.