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，似然方程通常需要迭代求解。我们研究了两种算法：一种避免大矩阵求逆的迭代比例缩放版本，在图稀疏时能提升速度，并将其与基于凸对偶性并通过邻域坐标下降对协方差矩阵进行操作的算法（实质上对应零惩罚的图形套索）进行比较。对于大型稀疏图，该迭代比例缩放算法版本具有可行性且收敛性质简单。基于邻域坐标下降的算法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，这在变量数超过观测数时可能难以实现。