GLASD: A Loss-Function-Agnostic Global Optimizer for Robust Correlation Estimation under Data Contamination and Heavy Tails

Abstract: Robust correlation estimation is essential in high-dimensional settings, particularly when data are contaminated by outliers or exhibit heavy-tailed behavior. Many robust loss functions of practical interest-such as those involving truncation or redescending M-estimators-lead to objective functions that are inherently non-convex and non-differentiable. Traditional methods typically focus on a single loss function tailored to a specific contamination model and develop custom algorithms tightly coupled with that loss, limiting generality and adaptability. We introduce GLASD (Global Adaptive Stochastic Descent), a general-purpose black-box optimization algorithm designed to operate over the manifold of positive definite correlation matrices. Unlike conventional solvers, GLASD requires no gradient information and imposes no assumptions of convexity or smoothness, making it ideally suited for optimizing a wide class of loss functions-including non-convex, non-differentiable, or discontinuous objectives. This flexibility allows GLASD to serve as a unified framework for robust estimation under arbitrary user-defined criteria. We demonstrate its effectiveness through extensive simulations involving contaminated and heavy-tailed distributions, as well as a real-data application to breast cancer proteomic network inference, where GLASD successfully identifies biologically plausible interactions despite the presence of outliers. The proposed method is scalable, constraint-aware, and available as open-source software at GitHub.