  The pseudo-likelihood method is one of the most popular algorithms for
learning sparse binary pairwise Markov networks. In this paper, we formulate
the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic
regression problem. In this way, many insights and optimization procedures for
sparse logistic regression can be applied to the learning of discrete Markov
networks. Specifically, we use the coordinate descent algorithm for generalized
linear models with convex penalties, combined with strong screening rules, to
solve the pseudo-likelihood problem with $L_1$ regularization. Therefore a
substantial speedup without losing any accuracy can be achieved. Furthermore,
this method is more stable than the node-wise logistic regression approach on
unbalanced high-dimensional data when penalized by small regularization
parameters. Thorough numerical experiments on simulated data and real world
data demonstrate the advantages of the proposed method.
