Representation Learning for Extremes

Extreme events are potentially catastrophic events that occur infrequently within an observation time frame, and it is necessary to understand the distribution of these events to properly plan for them. Extreme value theory provides a theoretical framework for extrapolating to the tails of a distribution using limited observations. However, for high-dimensional data such as images, covariates are generally not extreme but perhaps the features are extreme. In this work, we propose a framework for learning representations according to properties of extreme value theory. Specifically, we use the max-stability property of extreme value distributions to inform the representations of the model such that they extrapolate to the rare data observations. We theoretically characterize the properties of the model and provide an identifiability result for the parameters of the latent distribution. Our preliminary results suggest the promise of the method for extrapolating to regions of the distribution with little density.