Discovering Nonlinear Drivers of Extremes Using Rényi Transfer Entropy and Flexible Density Modeling

Thomas M. Menino Convention & Exhibition Center 

Understanding the hidden drivers of extreme spatio-temporal behavior requires information-theoretic
tools that move beyond linear dependence and Gaussian assumptions. We develop a
tail-emphasized approach for detecting directional interactions in complex environmental processes
using Rényi transfer entropy, a measure that highlights information flow arising from rare
but influential events. To estimate the required conditional densities, we use Mixture Density
Networks (MDNs), which can represent heavy-tailed and multimodal structures and therefore
capture both bulk behavior and extremes. Our current analysis applies this framework to daily
maximum temperature from Pacific Northwest stations, together with complementary drought
and circulation indices. The ultimate aim is to use the discovered nonlinear and tail-sensitive
relationships to inform parsimonious spatio–temporal models that better represent the mechanisms
underlying extreme environmental responses.

Rényi Transfer Entropy

Mixture Density Networks (MDNs)

Extreme events

Nonlinear dependence

Spatio-temporal climate dynamics

Information-theoretic causality 

Section on Statistics and the Environment