Bayesian extreme learning

A Bayesian Extreme Learning (BEL) framework is developed to address fundamental challenges in extreme value analysis: sparsity of extremes, the curse of dimensionality, and outlier contamination. BEL integrates extreme value filtering, information-theoretic regularization, and sequential Bayesian updating to enable robust inference on high-dimensional extremal dependence structures. Theoretically, I establish minimax optimal convergence rates and dimension-agnostic posterior concentration through a novel entropy regularization mechanism. Practically, BEL demonstrates superior performance in financial risk modeling and high-dimensional failure analysis. Empirical validation across economic sectors shows BEL's regularization prevents overfitting while maintaining interpretability for regulatory compliance. The framework's information bottleneck design, which explicitly optimizes the trade-off between tail fidelity and model complexity, provides a unified solution for expert systems requiring operational robustness in extreme scenarios.