Modeling Spatial Extremes via Ensemble-of-Trees of Pairwise Copulas

Assessing the risk of extreme events in a spatial domain, such as hurricanes, floods, and droughts, presents a unique significance in practice. Unfortunately, the existing extreme-value statistical models are typically not feasible for practical large-scale problems. Graphical models, on the other hand, are capable of handling sizable number of variables, but have yet to be explored in the realm of extreme-value analysis. To bridge the gap, an extreme-value graphical model is introduced in this paper, i.e., an ensemble-of-trees of pairwise copulas (ETPC). In the proposed graphical model, extreme-value marginal distributions are stitched together by means of a pairwise copulas, which in turn are the building blocks of the ensemble of trees. Novel linear-complexity stochastic gradient-based algorithms are then developed for learning the ETPC model and inferring missing data. As a result, the ETPC model is applicable to extreme-value problems with thousands of variables. It can be proven that, under mild conditions, the ETPC model exhibits the favorable property of tail-dependence between an arbitrary pair of sites (variables); consequently, the model is able to reliably capture statistical dependence between extreme values at different sites. Experimental results for both synthetic and real data demonstrate the advantages of the ETPC model in modeling fitting, imputation, and computational efficiency.