Applied Mathematics Department Colloquium - Christopher Wikle

Christopher Wikle, Department of Statistics, University of Missouri

Flexible and Efficient Spatial Extremes Estimation and Emulation via Variational Autoencoders

The world is full of extreme events.  For example, a central question in public health planning might be to assess the likelihood of extreme exposures (meteorological conditions, air pollution, social stress, etc.).  Such extreme events typically occur in spatial and/or temporal clusters.  Yet, the principal methodologies that statisticians deal with spatially dependent processes (Gaussian processes and Markov random fields) are not suitable for complex tail dependence structures. This is particularly true of simulation model emulation.  More flexible spatial extremes models exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from in high dimensions. Here I present recent work where we develop a new spatial extremes model that has flexible and non-stationary dependence properties, and we integrate it in the encoding-decoding structure of a variational autoencoder (XVAE), whose parameters are estimated via variational Bayes combined with deep learning. The XVAE can be used to analyze high-dimensional data or as a spatio-temporal emulator that characterizes the distribution of potential mechanistic model output states and produces outputs that have the same statistical properties as the inputs, especially in the tail. Through extensive simulation studies, we show that our XVAE is substantially more time-efficient than traditional Bayesian inference while also outperforming many spatial extremes models with a stationary dependence structure.  We demonstrate our method applied to a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea and to a high-resolution simulation model of a turbulent plume, such as one would find in a wildfire.  We note, however, that these methods can be applied to any data set or simulation model that exhibits extremes.

This is joint work with Likun Zhang and Xiaoyu Ma (University of Missouri), Raphael Huser (KAUST), and Kiran Bhaganagar (University of Texas-San Antonio). 

Primary References: https://arxiv.org/abs/2307.08079 , https://arxiv.org/abs/2502.04685