Estimation of Sparse Binary Pairwise Markov Networks using Pseudo-likelihoods

We consider the problems of estimating the parameters as well as the structure of binary-valued Markov networks. For maximizing the penalized log-likelihood, we implement an approximate procedure based on the pseudo-likelihood of Besag (1975) and generalize it to a fast exact algorithm. The exact algorithm starts with the pseudo-likelihood solution and then adjusts the pseudo-likelihood criterion so that each additional iterations moves it closer to the exact solution. Our results show that this procedure is faster than the competing exact method proposed by Lee, Ganapathi, and Koller (2006a). However, we also find that the approximate pseudo-likelihood as well as the approaches of Wainwright et al. (2006), when implemented using the coordinate descent procedure of Friedman, Hastie, and Tibshirani (2008b), are much faster than the exact methods, and only slightly less accurate.