Reviews: Sparse Logistic Regression Learns All Discrete Pairwise Graphical Models

This paper gives a simple and elegant algorithm for solving the long-studied problem of graphical model estimation (at least, in the case of pairwise MRFs, which includes the classic Ising model). The method uses a form of constrained logistic regression, which in retrospect, feels like the "right" way to solve this problem. The algorithm simply runs this constrained logistic regression method to learn the outgoing edges attached to each node. The proof is elegant and modular: first, based on standard generalization bounds, a sufficient number of samples allows minimization of the logistic loss function. Second, this loss is related to another loss function (the sigmoid of the inner product of the parameter vector with a sample from the distribution).