  Mitigating the risk arising from extreme events is a fundamental goal with
many applications, such as the modelling of natural disasters, financial
crashes, epidemics, and many others. To manage this risk, a vital step is to be
able to understand or generate a wide range of extreme scenarios. Existing
approaches based on Generative Adversarial Networks (GANs) excel at generating
realistic samples, but seek to generate typical samples, rather than extreme
samples. Hence, in this work, we propose ExGAN, a GAN-based approach to
generate realistic and extreme samples. To model the extremes of the training
distribution in a principled way, our work draws from Extreme Value Theory
(EVT), a probabilistic approach for modelling the extreme tails of
distributions. For practical utility, our framework allows the user to specify
both the desired extremeness measure, as well as the desired extremeness
probability they wish to sample at. Experiments on real US Precipitation data
show that our method generates realistic samples, based on visual inspection
and quantitative measures, in an efficient manner. Moreover, generating
increasingly extreme examples using ExGAN can be done in constant time (with
respect to the extremeness probability $\tau$), as opposed to the
$\mathcal{O}(\frac{1}{\tau})$ time required by the baseline approach.
