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Title: Approximating spatial extreme value processes with deep learning Authors:  Reetam Majumder - North Carolina State University (United States) [presenting]
Brian Reich - North Carolina State University (United States)
Benjamin Shaby - Colorado State University (United States)
Abstract: The Intergovernmental Panel on Climate Change has projected an increased frequency of hydroclimatic extremes in its Sixth Assessment released in 2021. Quantifying how the probability and magnitude of extreme flooding events are changing is key to mitigating their impacts. While climate data are inherently spatially dependent, spatial models such as Gaussian processes (GP) do not adequately model extreme events, and theoretically-justified extreme value analysis models like the max-stable process (MSP) give intractable likelihoods. We propose a process mixture model which specifies spatial dependence in extreme values as a convex combination of a GP and an MSP, using a deep learning model to approximate the likelihood. We propose a unique computational strategy where a feed-forward neural network is embedded in a density regression model to approximate the conditional distribution at one spatial location given a set of neighbors. We then use this univariate density function to approximate the joint likelihood for all locations by way of a Vecchia approximation. The process mixture model is used to analyze changes in annual maximum streamflow within the US over the last 50 years, and is able to detect areas which show increases in extreme streamflow over time.