# Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk

arXiv: https://arxiv.org/abs/2208.07590 · HTML: https://mlsanity.com/paper/2208.07590/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 58 references that are in the map.
- First posted on arXiv 16 Aug 2022.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Gradient boosting for extreme quantile regression](https://mlsanity.com/paper/2103.00808/) (2021)
- [Extremes on river networks](https://mlsanity.com/paper/1501.02663/) (2015)
- [Extremal Random Forests](https://mlsanity.com/paper/2201.12865/) (2022)
- [Improving precipitation forecasts using extreme quantile regression](https://mlsanity.com/paper/1806.05429/) (2018)
- [A horse racing between the block maxima method and the peak-over-threshold approach](https://mlsanity.com/paper/1807.00282/) (2018)

## Built on by (most cited first, 19 of 19)

- [Validating Deep Learning Weather Forecast Models on Recent High-Impact Extreme Events](https://mlsanity.com/paper/2404.17652/) (2024)
- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [A VAE Approach to Sample Multivariate Extremes](https://mlsanity.com/paper/2306.10987/) (2023)
- [Deep graphical regression for jointly moderate and extreme Australian wildfires](https://mlsanity.com/paper/2308.14547/) (2023)
- [Neural Bayes estimators for censored inference with peaks-over-threshold models](https://mlsanity.com/paper/2306.15642/) (2023)
- [Progression: an extrapolation principle for regression](https://mlsanity.com/paper/2410.23246/) (2024)
- [Deep Learning of Multivariate Extremes via a Geometric Representation](https://mlsanity.com/paper/2406.19936/) (2024)
- [Extreme Conformal Prediction: Reliable Intervals for High-Impact Events](https://mlsanity.com/paper/2505.08578/) (2025)
- [Insights into the drivers and spatio-temporal trends of extreme Mediterranean wildfires with statistical deep-learning](https://mlsanity.com/paper/2212.01796/) (2022)
- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [Distributional Regression U-Nets for the Postprocessing of Precipitation Ensemble Forecasts](https://mlsanity.com/paper/2407.02125/) (2024)
- [Deep learning joint extremes of metocean variables using the SPAR model](https://mlsanity.com/paper/2412.15808/) (2024)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Data-driven rainfall prediction at a regional scale: a case study with Ghana](https://mlsanity.com/paper/2410.14062/) (2024)
- [Neural Bayes estimation and selection for complex bivariate extremal dependence models](https://mlsanity.com/paper/2503.23156/) (2025)
- [Uncertainty Quantification in SVM prediction](https://mlsanity.com/paper/2505.15429/) (2025)
- [QDeepGR4J: Quantile-based ensemble of deep learning and GR4J hybrid rainfall-runoff models for extreme flow prediction with uncertainty quantification](https://mlsanity.com/paper/2510.05453/) (2025)
- [Stop Suppressing the Tail: Causal Inference for Extreme Events](https://mlsanity.com/paper/2605.27474/) (2026)
- [Gradient boosting for extremes: sampling theory and application to insurance](https://mlsanity.com/paper/2606.14268/) (2026)

## Abstract (arXiv)

Risk assessment for extreme events requires accurate estimation of high quantiles that go beyond the range of historical observations. When the risk depends on the values of observed predictors, regression techniques are used to interpolate in the predictor space. We propose the EQRN model that combines tools from neural networks and extreme value theory into a method capable of extrapolation in the presence of complex predictor dependence. Neural networks can naturally incorporate additional structure in the data. We develop a recurrent version of EQRN that is able to capture complex sequential dependence in time series. We apply this method to forecast flood risk in the Swiss Aare catchment. It exploits information from multiple covariates in space and time to provide one-day-ahead predictions of return levels and exceedance probabilities. This output complements the static return level from a traditional extreme value analysis, and the predictions are able to adapt to distributional shifts as experienced in a changing climate. Our model can help authorities to manage flooding more effectively and to minimize their disastrous impacts through early warning systems.