# Estimating a Directed Tree for Extremes

arXiv: https://arxiv.org/abs/2102.06197 · HTML: https://mlsanity.com/paper/2102.06197/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 70 references that are in the map.
- First posted on arXiv 11 Feb 2021.

## Builds on (most cited first, 10 of 10)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [Causal discovery in heavy-tailed models](https://mlsanity.com/paper/1908.05097/) (2019)
- [Extremes on river networks](https://mlsanity.com/paper/1501.02663/) (2015)
- [Structure learning for extremal tree models](https://mlsanity.com/paper/2012.06179/) (2020)
- [A continuous updating weighted least squares estimator of tail dependence in high dimensions](https://mlsanity.com/paper/1601.04826/) (2016)
- [Tail dependence of recursive max-linear models with regularly varying noise variables](https://mlsanity.com/paper/1701.07351/) (2017)
- [Bayesian Networks for Max-linear Models](https://mlsanity.com/paper/1901.03948/) (2019)
- [Estimating an Extreme Bayesian Network via Scalings](https://mlsanity.com/paper/1912.03968/) (2019)
- [Open storm: a complete framework for sensing and control of urban watersheds](https://mlsanity.com/paper/1708.05172/) (2017)

## Built on by (most cited first, 5 of 5)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery](https://mlsanity.com/paper/2503.17037/) (2025)
- [Sortability of Time Series Data](https://mlsanity.com/paper/2407.13313/) (2024)
- [Inference for max-linear Bayesian networks with noise](https://mlsanity.com/paper/2505.00229/) (2025)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)

## Abstract (arXiv)

We propose a new method to estimate a root-directed spanning tree from extreme data. A prominent example is a river network, to be discovered from extreme flow measured at a set of stations. Our new algorithm utilizes qualitative aspects of a max-linear Bayesian network, which has been designed for modelling causality in extremes. The algorithm estimates bivariate scores and returns a root-directed spanning tree. It performs extremely well on benchmark data and new data. We prove that the new estimator is consistent under a max-linear Bayesian network model with noise. We also assess its strengths and limitations in a small simulation study.