# Extremes on river networks

arXiv: https://arxiv.org/abs/1501.02663 · HTML: https://mlsanity.com/paper/1501.02663/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2015.

## Built on by (most cited first, 9 of 9)

- [Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk](https://mlsanity.com/paper/2208.07590/) (2022)
- [A VAE Approach to Sample Multivariate Extremes](https://mlsanity.com/paper/2306.10987/) (2023)
- [Estimating a Directed Tree for Extremes](https://mlsanity.com/paper/2102.06197/) (2021)
- [Extreme Conformal Prediction: Reliable Intervals for High-Impact Events](https://mlsanity.com/paper/2505.08578/) (2025)
- [Extremal graphical modeling with latent variables via convex optimization](https://mlsanity.com/paper/2403.09604/) (2024)
- [Inference for max-linear Bayesian networks with noise](https://mlsanity.com/paper/2505.00229/) (2025)
- [Modelling and simulating spatial extremes by combining extreme value theory with generative adversarial networks](https://mlsanity.com/paper/2111.00267/) (2021)
- [A PC Algorithm for Max-Linear Bayesian Networks](https://mlsanity.com/paper/2508.13967/) (2025)
- [Out-of-Distribution generalization of quantile regression with heavy tailed inputs: an SVM approach](https://mlsanity.com/paper/2606.00265/) (2026)

## Abstract (arXiv)

Max-stable processes are the natural extension of the classical extreme-value distributions to the functional setting, and they are increasingly widely used to estimate probabilities of complex extreme events. In this paper we broaden them from the usual situation in which dependence varies according to functions of Euclidean distance to situations in which extreme river discharges at two locations on a river network may be dependent because the locations are flow-connected or because of common meteorological events. In the former case dependence depends on river distance, and in the second it depends on the hydrological distance between the locations, either of which may be very different from their Euclidean distance. Inference for the model parameters is performed using a multivariate threshold likelihood, which is shown by simulation to work well. The ideas are illustrated with data from the upper Danube basin.