Neural learning for extreme values

2024-11-13 — 2024-11-13

Wherein neural methods for modelling extremes are examined, and the complications of spatial dependence and copula-linked correlations are set forth, while singular rare occurrences are noted.

density
dynamical systems
machine learning
neural nets
point processes
probability
sciml
SDEs
signal processing
spatial
statistics
stochastic processes
tail risk
time series
Figure 1

At the intersection of extreme value theory and neural networks — When can we make neural nets model rare extremes well?

This is a subtle problem. Extremal values are hard to estimate in general for a bunch of obvious and less obvious reasons.

The risks you care about you might only see once. The distributions of the risk might be correlated in difficult ways, even spatially in ways that are challenging for neural nets even before we worry about the classical risk management.

But! Apparently, there are things that can be done!

TBC

1 References

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Majumder, and Reich. 2023. “A Deep Learning Synthetic Likelihood Approximation of a Non-Stationary Spatial Model for Extreme Streamflow Forecasting.” Spatial Statistics.
Pasche, and Engelke. 2024. “Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk.” The Annals of Applied Statistics.
Richards, and Huser. 2024. “Regression Modelling of Spatiotemporal Extreme U.S. Wildfires via Partially-Interpretable Neural Networks.”
Richards, and Huser. n.d. “A Unifying Partially-Interpretable Framework for Neural Network-Based Extreme Quantile Regression.”
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