In a world where climate change is causing more and more extreme weather events of increasing magnitude, the study of such phenomena has become essential for risk management in many fields such as climate sciences or finance. While classical statistical learning tools can be useful to address these problems, they must first be adapted to the specific context of extreme value analysis.
In this presentation, we first introduce a probabilistic framework for regression in regions where the input variable is extreme, in contrast to classical approaches that typically focus on regions where the output variable is extreme. We establish theoretical results on risks and regression functions in these extreme regions, and propose an adapted learning algorithm.
In a second part, we apply this algorithm to the prediction of extreme sea levels along the French Atlantic coast. The goal is to predict sea levels at a tide gauge station with a short observation record, by leveraging extreme data from nearby stations with longer historical records. This approach allows us to increase the available extreme data and then, to reduce the uncertainty of extreme estimates at the target station. Alongside our regression approach, we also implement another method based on multivariate extreme value theory, which can, for example, be used to generate synthetic samples of extreme sea levels.