A global approach for learning sparse Ising models
This work addresses the challenge of efficiently learning binary-valued pairwise Markov models for applications in fields like statistical physics or network analysis, but it appears incremental as it builds on existing l1-regularized approaches with a global twist.
The authors tackled the problem of learning sparse Ising models by proposing a global estimation method using l1-regularized logistic regression, which simultaneously learns all edges and link parameters, and numerical experiments confirmed its advantages.
We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. Under sparsity assumption, we propose a method based on $l_1$- regularized logistic regression, which estimate globally the whole set of edges and link parameters. Unlike the more recent methods discussed in literature that learn the edges and the corresponding link parameters one node at a time, in this work we propose a method that learns all the edges and corresponding link parameters simultaneously for all nodes. The idea behind this proposal is to exploit the reciprocal information of the nodes between each other during the estimation process. Numerical experiments highlight the advantage of this technique and confirm the intuition behind it.