Fakhar et al. propose convex method for realistic correlation matrices

A team from Université Grenoble Alpes (UGA) and associated labs—Ali Fakhar, Kévin Polisano, Irène Gannaz, and Sophie Achard—has published a paper on a novel convex optimization framework for generating correlation matrices with user-defined sparsity patterns tied to graph structures. The approach projects an initial matrix onto an elliptope under a positive semidefiniteness constraint, with off-diagonal entries for missing edges fixed to zero and diagonal entries set to one. Beyond enforcing sparsity, the method uniquely allows control over the mean of the off-diagonal entry distribution, enabling the generation of correlation matrices that mimic realistic data more closely than existing techniques. The authors provide theoretical guarantees for solution existence both in the general case and under the additional mean constraint.

The framework is designed for benchmarking statistical methods for graphical model inference, not for uniform sampling. Simulation studies demonstrate how the generated matrices reflect the underlying graph structure. The method is applied to two real-world datasets—one from neuroscience and one from finance—and compared against GAN-based correlation matrix generation, showing superior controllability and theoretical rigor. This work falls under matrix completion and offers a principled, tunable tool for researchers needing realistic correlation matrices with known sparsity, particularly useful in fields like econometrics, network neuroscience, and any domain relying on Gaussian graphical models.