Robust Modeling of Extremes in the Presence of Inliers with Enhanced Tail Estimation

What the math gives to ML

The paper provides a transferable four-region likelihood that separates inliers, ordinary body observations, and extremes instead of forcing one residual distribution to explain all data. Its generalized Pareto tail gives a principled model for rare large residuals, while mixture weights estimate tail prevalence rather than fixing it through an arbitrary threshold. The most direct neural-network use is a differentiable tail-aware regression loss, with smooth threshold gates replacing the paper's hard indicators. This could improve calibration and robustness on datasets containing both near-zero failures and heavy-tailed errors.