Causal discovery in heavy-tailed models

Research output: Contribution to journalJournal articlepeer-review

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Causal discovery in heavy-tailed models. / Gnecco, Nicola; Meinshausen, Nicolai; Peters, Jonas; Engelke, Sebastian.

In: Annals of Statistics, Vol. 49, No. 3, 2021, p. 1755-1778.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Gnecco, N, Meinshausen, N, Peters, J & Engelke, S 2021, 'Causal discovery in heavy-tailed models', Annals of Statistics, vol. 49, no. 3, pp. 1755-1778. https://doi.org/10.1214/20-AOS2021

APA

Gnecco, N., Meinshausen, N., Peters, J., & Engelke, S. (2021). Causal discovery in heavy-tailed models. Annals of Statistics, 49(3), 1755-1778. https://doi.org/10.1214/20-AOS2021

Vancouver

Gnecco N, Meinshausen N, Peters J, Engelke S. Causal discovery in heavy-tailed models. Annals of Statistics. 2021;49(3):1755-1778. https://doi.org/10.1214/20-AOS2021

Author

Gnecco, Nicola ; Meinshausen, Nicolai ; Peters, Jonas ; Engelke, Sebastian. / Causal discovery in heavy-tailed models. In: Annals of Statistics. 2021 ; Vol. 49, No. 3. pp. 1755-1778.

Bibtex

@article{5a5d2e76d6624c41b1683150c290754d,
title = "Causal discovery in heavy-tailed models",
abstract = "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 nonextremal approaches in causal discovery on synthetic and real data. The code is available as an open-access R package.",
keywords = "Causality, Extreme value theory, Heavy-tailed distributions, Nonparametric estimation",
author = "Nicola Gnecco and Nicolai Meinshausen and Jonas Peters and Sebastian Engelke",
note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2021",
year = "2021",
doi = "10.1214/20-AOS2021",
language = "English",
volume = "49",
pages = "1755--1778",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

RIS

TY - JOUR

T1 - Causal discovery in heavy-tailed models

AU - Gnecco, Nicola

AU - Meinshausen, Nicolai

AU - Peters, Jonas

AU - Engelke, Sebastian

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2021

PY - 2021

Y1 - 2021

N2 - 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 nonextremal approaches in causal discovery on synthetic and real data. The code is available as an open-access R package.

AB - 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 nonextremal approaches in causal discovery on synthetic and real data. The code is available as an open-access R package.

KW - Causality

KW - Extreme value theory

KW - Heavy-tailed distributions

KW - Nonparametric estimation

UR - http://www.scopus.com/inward/record.url?scp=85113139684&partnerID=8YFLogxK

U2 - 10.1214/20-AOS2021

DO - 10.1214/20-AOS2021

M3 - Journal article

AN - SCOPUS:85113139684

VL - 49

SP - 1755

EP - 1778

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 3

ER -

ID: 278042827