1Extreme-Value Graphical Models with Multiple Covariates

Abstract—To assess the risk of extreme events such as hurri-canes, earthquakes, and floods, it is crucial to develop accurate extreme-value statistical models. Extreme events often display heterogeneity (i.e., non-stationarity), varying continuously with a number of covariates. Previous studies have suggested that models considering covariate effects lead to reliable estimates of extreme events distributions. In this paper, we develop a novel statistical 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 storm direction. In the proposed model, the block maximum 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, in particular, a three-dimensional (3D) thin-membrane model. Efficient learning and inference algorithms are developed based on the special characteristics of the thin-membrane model. We further show how to extend the model to incorporate an arbitrary number of covariates in a straightforward manner. Numerical results for both synthetic and real data indicate that the proposed model can accurately describe marginal behaviors of extreme events. Index Terms—extreme events modeling, Gaussian graphical models, covariates, Laplacian matrix, Kronecker produc