Asymptotic Properties of the Joint Neighborhood Selection Method for Estimating Categorical Markov Networks

The joint neighborhood selection method was proposed as a fast algorithm to estimate parameters of a Markov network for binary variables and identify the underlying graphical model. This paper shows that this method leads to consistent parameter estimation and model selection under high-dimensional asymptotics. We also apply the algorithm to the voting records of US senators to illustrate the kinds of conclusions one can obtain from this procedure; our analysis confirms known political patterns and provides new insights into the associations between senators. We also show how to extend the joint neighborhood selection method to general categorical variables with more than two levels.