A Simple Method for Estimating Gaussian Graphical Models

The penalized likelihood estimator is the state-of-the-art method for estimating a Gaussian graphical model, because it delivers a symmetric graph and is efficient to compute owing to the graphical lasso implementation.However, the penalized likelihood estimator requires a stringent irrepresentability condition in order to achieve consistent recovery of the underlying graph.Another popular method, neighborhood selection, does not offer a symmetric solution by itself and also requires a set of irrepresentability conditions for the exact recovery.In this paper we propose a new method named simple graph maker for estimating the underlying graph.The simple graph maker produces a symmetric estimator via a simple 1 penalized quadratic problem, which is easily computed by coordinate descent.The simple graph maker is shown to recover the underlying graph with overwhelming probability without assuming additional structure conditions on the variables.The rates of convergence under various matrix norms are also established.The new method is shown to have excellent performance on simulated and real data.