# Causal discovery in heavy-tailed models

arXiv: https://arxiv.org/abs/1908.05097 · HTML: https://mlsanity.com/paper/1908.05097/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2019.

## Built on by (most cited first, 20 of 20)

- [Root Cause Analysis of Outliers with Missing Structural Knowledge](https://mlsanity.com/paper/2406.05014/) (2024)
- [Learning linear non-Gaussian directed acyclic graph with diverging number of nodes](https://mlsanity.com/paper/2111.00740/) (2021)
- [Estimating a Directed Tree for Extremes](https://mlsanity.com/paper/2102.06197/) (2021)
- [Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm](https://mlsanity.com/paper/2405.18314/) (2024)
- [Regular Variation in Hilbert Spaces and Principal Component Analysis for Functional Extremes](https://mlsanity.com/paper/2308.01023/) (2023)
- [AI for Extreme Event Modeling and Understanding: Methodologies and Challenges](https://mlsanity.com/paper/2406.20080/) (2024)
- [Cross-validating causal discovery via Leave-One-Variable-Out](https://mlsanity.com/paper/2411.05625/) (2024)
- [Efficient Differentiable Discovery of Causal Order](https://mlsanity.com/paper/2410.08787/) (2024)
- [Kernel PCA for multivariate extremes](https://mlsanity.com/paper/2211.13172/) (2022)
- [Towards Dynamic Causal Discovery with Rare Events: A Nonparametric Conditional Independence Test](https://mlsanity.com/paper/2211.16596/) (2022)
- [TSLiNGAM: DirectLiNGAM under heavy tails](https://mlsanity.com/paper/2308.05422/) (2023)
- [Estimation of Treatment Effects in Extreme and Unobserved Data](https://mlsanity.com/paper/2506.14051/) (2025)
- [Stop Suppressing the Tail: Causal Inference for Extreme Events](https://mlsanity.com/paper/2605.27474/) (2026)
- [Formalizing and falsifying causal pathways of rare events](https://mlsanity.com/paper/2605.31254/) (2026)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)
- [Interpretable Causal Discovery via Causal-Effect Constraints](https://mlsanity.com/paper/2608.12640/) (2026)
- [GFCM: A Tail-Sensitive Mixed-Type Conditional Independence Test for Causal Discovery](https://mlsanity.com/paper/2608.15332/) (2026)
- [A Location-Invariant Estimator of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions](https://mlsanity.com/paper/2609.04018/) (2026)
- [Local Fisher Information Enables Sparse Causal Discovery](https://mlsanity.com/paper/2610.04291/) (2026)
- [DAG Structure Learning with Node-Varying Heavy-Tailed Disturbances](https://mlsanity.com/paper/2610.13304/) (2026)

## Abstract (arXiv)

Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest themselves in extremes. This work aims to connect the two fields of causal inference and extreme value theory. We define the causal tail coefficient that captures asymmetries in the extremal dependence of two random variables. In the population case, the causal tail coefficient is shown to reveal the causal structure if the distribution follows a linear structural causal model. This holds even in the presence of latent common causes that have the same tail index as the observed variables. Based on a consistent estimator of the causal tail coefficient, we propose a computationally highly efficient algorithm that estimates the causal structure. We prove that our method consistently recovers the causal order and we compare it to other well-established and non-extremal approaches in causal discovery on synthetic and real data. The code is available as an open-access R package.