In the fourth installment of the Generative AI for Extreme Events conference, Christian Y. Robert delivered a comprehensive overview of Extreme Value Theory (EVT), emphasizing why standard statistical models fall short for rare, high-impact events.
Robert opened by highlighting the importance of extreme events across finance, insurance, climate science, and engineering—domains where data on catastrophes is sparse, dependence structures are complex, and accurate modeling is critical. He argued that generative AI must go beyond reproducing typical observations and instead respect tail behavior, extremal dependence, clustering, and the structure of rare episodes.
The presentation was structured in three parts. First, Robert covered univariate EVT, including maxima, record values, threshold exceedances, and the foundational Generalized Extreme Value (GEV) and Generalized Pareto (GPD) distributions. The second part tackled multivariate extremes: componentwise maxima, tail dependence, max-stable distributions, and spectral measures. The third part extended to infinite-dimensional settings, such as spatial–temporal fields modeled with max-stable and generalized Pareto processes, plus the radius-shape decomposition of extreme episodes.
Finally, Robert introduced the point process viewpoint as a unifying framework for exceedances, Poisson limits, clustering, and the extremal index. He underscored its connection to generative modeling, noting that effective AI for extremes must incorporate these probabilistic tools to avoid underestimating tail risks.
This talk serves as a valuable primer for researchers and practitioners seeking robust methods for modeling and generating extreme events using AI.