Joint Structure Estimation for Categorical Markov Networks

We consider the problem of identifying and estimating non-zero parameters in the Markov model for binary variables. We approximate the full likelihood by a pseudolikelihood function and propose a joint `1-penalized logistic regression method, which imposes overall sparsity on the parameters. We show that the proposed method leads to consistent parameter estimation and model selection under high-dimensional asymptotics, and we develop an efficient local quadratic approximation algorithm for computing the estimator. The proposed method is used to explore voting dependencies between senators in the 109th Congress; our analysis confirms known political patterns and provides new insights into the US Senate’s voting.