Leveraging Standardization in Graph Learning
Résumé
Standardization of the variables is a staple scaling tool that can be beneficial in most statistical learning tasks. In the context of graph learning, we propose to take further advantage of this pre-processing, as it yields an additional implicit normalization structure for the covariance matrix. For Gaussian graphical models, we propose a new algorithm that aims at estimating a sparse precision matrix while its inverse is constrained to be a (possibly low-rank structured) correlation matrix. The corresponding optimization problem is addressed by using the framework of Riemannian optimization. Simulations over various graph structures illustrate the interest of the proposed approach.
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