Causal discovery in heavy-tailed models
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
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 journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
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