A block coordinate descent algorithm for sparse Gaussian graphical model inference with laplacian constraints

We consider the problem of inferring sparse Gaussian graphical models with Laplacian constraints, which can also be viewed as learning a graph Laplacian such that the observed graph signals are smooth with respect to it. A block coordinate descent algorithm is proposed for the resulting linearly constrained log-determinant maximum likelihood estimation problem with sparse regularization. Simulation results on synthetic data show the efficiency of our proposed algorithm.