A recent conference on generative AI for extreme events brought together experts to discuss how probabilistic tools can better model rare, high-impact phenomena. Part II of the event, led by Christian Y. Robert, offered a comprehensive overview of Extreme Value Theory (EVT) for heavy tails and rare events.
Robert emphasized that standard statistical modeling often fails for extremes because such events are scarce, poorly observed, and frequently exhibit strong dependencies across time, space, or variables. The presentation covered univariate EVT foundations—including GEV and GPD distributions—before moving to multivariate extremes, which involve tail dependence, max-stable distributions, and spectral measures.
A significant portion addressed infinite-dimensional settings, where extreme events are modeled as functions or spatial-temporal fields using max-stable processes and generalized Pareto processes. Robert also highlighted the point process viewpoint, which unifies exceedances, Poisson limits, and clustering of extremes, and noted its connection to generative modeling.
The talk underscored the importance of specialized probabilistic methods for fields like finance, insurance, climate science, and engineering, where understanding the tails of distributions is critical for risk mitigation.