Extreme-value graphical models with multiple covariates

Hang Yu, Jingjing Cheng, Justin Dauwels

Abstract: To assess the risk of extreme events such as hurricanes and floods, it is crucial to develop accurate extreme-value statistical models. Extreme events often display heterogeneity, varying continuously with a number of covariates. Previous studies have suggested that models considering covariate effects lead to reliable estimates of extreme value distributions. In this paper, we develop a novel model to incorporate the effects of multiple covariates. Specifically, we analyze as an example the extreme sea states in the Gulf of Mexico, where the distribution of extreme wave heights changes systematically with location and wind direction. The block maxima at each location and sector of wind direction are assumed to follow the Generalized Extreme Value (GEV) distribution. The GEV parameters are coupled across the spatio-directional domain through a graphical model, particularly, a multidimensional thin-membrane model. Efficient learning and inference algorithms are then developed based on the special characteristics of the thin-membrane model. Numerical results for both synthetic and real data indicate that the proposed model can accurately describe marginal behavior of extreme events.