Abstract
Extreme value statistics concerns the maxima of random variables and relations between the tails of distributions rather than averages and correlations. The vast majority of models are centered around {max-stable distributions}, the Gaussian analogs for extremes. However, max-stable multivariate have an intractable likelihood, severely limiting statistical learning and inference. Directed graphical models for extreme values (aka max-linear Bayesian networks) have only appeared in 2018, but have seen many applications in finance, hydrology and extreme risks modelling. This talk (1) highlights how they differ from usual Bayesian networks, (2) discusses their connections to tropical convex geometry and k-SAT, (3) shows performances of current learning algorithms on various hydrology datasets, and (4) outlines major computational and statistical challenges in fitting such models to data.