Latent tree ensemble of pairwise copulas for spatial extremes analysis

We consider the problem of jointly describing extreme events at a multitude of locations, which presents paramount importance in catastrophes forecast and risk management. Specifically, a novel Ensemble-of-Latent-Trees of Pairwise Copula (ELTPC) model is proposed. In this model, the spatial dependence is captured by latent trees expressed by pairwise copulas. To compensate the limited expressiveness of every single latent tree, an mixture of latent trees is employed. By harnessing the variational inference and stochastic gradient techniques, we further develop a triply stochastic variational inference (TSVI) algorithm for learning and inference. The corresponding computational complexity is only linear in the number of variables. Numerical results from both the synthetic and real data show that the ELTPC model provides a reliable description of the spatial extremes in a flexible but parsimonious manner.