# A global approach for learning sparse Ising models

## TL;DR

This paper introduces a global method using $l_1$-regularized logistic regression to simultaneously learn the structure and parameters of sparse Ising models, improving over node-wise approaches by leveraging reciprocal node information.

## Contribution

The paper presents a novel global estimation approach for sparse Ising models that estimates all edges and parameters simultaneously, unlike existing node-wise methods.

## Key findings

- The proposed method effectively learns sparse Ising models.
- Numerical experiments demonstrate the advantage of the global approach.
- The method exploits reciprocal node information during estimation.

## Abstract

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.