  In many applications of time series models, such as climate analysis and
social media analysis, we are often interested in extreme events, such as
heatwave, wind gust, and burst of topics. These time series data usually
exhibit a heavy-tailed distribution rather than a Gaussian distribution. This
poses great challenges to existing approaches due to the significantly
different assumptions on the data distributions and the lack of sufficient past
data on extreme events. In this paper, we propose the Sparse-GEV model, a
latent state model based on the theory of extreme value modeling to
automatically learn sparse temporal dependence and make predictions. Our model
is theoretically significant because it is among the first models to learn
sparse temporal dependencies among multivariate extreme value time series. We
demonstrate the superior performance of our algorithm to the state-of-art
methods, including Granger causality, copula approach, and transfer entropy, on
one synthetic dataset, one climate dataset and two Twitter datasets.
