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.

翻译：在高斯图模型中，似然方程通常需通过迭代方法求解。本文研究了两种算法：一种改进的比例迭代算法避免了大型矩阵求逆，从而在处理稀疏图时提升了运算速度；另一种基于凸对偶性的算法通过对协方差矩阵进行邻域坐标下降操作，实质上对应于零惩罚的图形套索。对于大型稀疏图，改进的比例迭代算法具有可行性且收敛性质简单。基于邻域坐标下降的算法运算速度极快且对稀疏性的依赖较小，但需要正定初始值才能收敛，当变量数超过观测数时这一点可能难以实现。