Deep Extreme Value Copulas for Estimation and Sampling

Modeling the occurrence of extreme events is an important task in many disciplines, such as medicine, environmental science, engineering, and finance. For example, understanding the probability of a patient having an adverse reaction to medication or the distribution of economic shocks is critical to mitigating the associated effects of these events. However, these events are rare in occurrence and often difficult to characterize with traditional statistical tools. This has been the primary focus of extreme value theory (EVT), which describes how to extrapolate the occurrence of rare events outside the range of available data [1]. In the one-dimensional case, EVT provides remarkably simple models for the distribution of the maximum of an infinite number of independent and identically distributed (i.i.d) random variables.