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We consider the problem of learning the link parameters as well as thestructure of a binary-valued pairwise Markov model. Under sparsity assumption,we propose a method based on $l_1$- regularized logistic regression, whichestimate globally the whole set of edges and link parameters. Unlike the morerecent methods discussed in literature that learn the edges and thecorresponding link parameters one node at a time, in this work we propose amethod that learns all the edges and corresponding link parameterssimultaneously for all nodes. The idea behind this proposal is to exploit thereciprocal information of the nodes between each other during the estimationprocess. Numerical experiments highlight the advantage of this technique andconfirm the intuition behind it.

A global approach for learning sparse Ising models