Universality of High-Dimensional Logistic Regression and a Novel CGMT under Dependence with Applications to Data Augmentation

Understand

Over the last decade, a wave of research has characterized the exact asymptotic risk of many high-dimensional models in the proportional regime.

• Two foundational results have driven this progress: Gaussian universality, which shows that the asymptotic risk of estimators trained on non-Gaussian and Gaussian data is equivalent, and the convex Gaussian min-max theorem (CGMT), which characterizes the risk under Gaussian settings.
• However, these results rely on the assumption that the data consists of independent random vectors--an assumption that significantly limits its applicability to many practical setups.
• In this paper, we address this limitation by generalizing both results to the dependent setting.