Learning Markov Network Structure using Brownian Distance Covariance

Undirected graphical models, also known as Markov random fields or Markov networks, have become a part of the mainstream of statistical theory and application in recent years. These models use graphs to represent conditional independences among sets of random variables. In these graphs, the absence of an edge between two vertices means the corresponding random variables are conditionally independent, given the other variables. Learning the structure of a graph is equivalent to learning if there exists an edge between every pair of nodes in the graph. In the past decade, significant progress has been made on designing efficient algorithms to learn undirected graphs from high-dimensional observational datasets. Most of these methods are based on either the penalized maximum-likelihood estimation or penalized regression methods. Works has focused on the problem of estimating the graph in this high dimensional setting, which becomes feasible if graph is sparse.