Learning binary undirected graph in low dimensional regime

Given a random sample drawn from a Multivariate Bernoulli Variable (MBV), we consider the problem of estimating the structure of the undirected graph for which the distribution is pairwise Markov and the parameters' vector of its exponential form. We propose a simple method that provides a closed form estimator of the parameters' vector and through its support also provides an estimate of the undirected graph associated with the MBV distribution. The estimator is proved to be asymptotically consistent but it is feasible only in low-dimensional regimes. Synthetic examples illustrate its performance compared with another method that represents state of the art in literature. Finally, the proposed procedure is used to analyze a data set in the pediatric allergology area showing its practical efficiency.