Efficient neighborhood selection for walk summable Gaussian graphical models

This paper addresses the problem of learning Gaussian graphical models using a threshold-based greedy neighborhood selection and pruning algorithm. The algorithm leverages the fact that the maximum conditional covariance between a node and its undiscovered neighbors given any estimated neighborhood is always bounded away from zero. We provide theoretical guarantees for the efficiency and accuracy of our algorithm for the class of walk summable Gaussian graphical models. We verify the performance of the algorithm through simulations.