A Generalized Gaussian Min–Max Framework Inferring Post-Processing Effects in High-Dimensional Estimation

Overview

Statistical analysis of high-dimensional stochastic optimization is central to modern signal processing and machine learning. When problem dimensions grow simultaneously, a key question is how the optimal cost and the solution distribution behave, as these govern many performance metrics of practical interest. In practice, however, the nominal solutions are often unusable due to hardware or physical constraints. This talk introduces the Convex Gaussian Min–Max Theorem (CGMT) as a principled framework to analyze the performance of such solutions, and presents a new Gordon-type inequality to study functionals of the solutions that arise when direct deployment is infeasible. While our case study focuses on downlink precoder design, the methodology is broadly applicable beyond precoding.