Separation-based causal discovery for extremes

TL;DR

This paper introduces XSCMs, a new class of causal models tailored for extreme events, enabling causal discovery in heavy-tailed and tail-dependent data using separation-based tests.

Contribution

The paper develops XSCMs that extend traditional SCMs to model and infer causal structures among extreme values, with theoretical guarantees and practical algorithms.

Findings

XSCMs satisfy causal Markov and faithfulness properties for extremes.

Separation-based tests enable DAG estimation among tail-dependent variables.

Method validated on simulations, river data, and China's derivatives market.

Abstract

Structural causal models (SCMs), with an underlying directed acyclic graph (DAG), provide a powerful analytical framework to describe the interaction mechanisms in large-scale complex systems. However, when the system exhibits extreme events, the governing mechanisms can change dramatically, and SCMs with a focus on rare events are needed. We propose a new class of SCMs, called XSCMs, which leverage transformed-linear algebra to model causal relationships among extreme values. Similar to traditional SCMs, we prove that XSCMs satisfy the causal Markov and causal faithfulness properties with respect to partial tail (un)correlatedness. This enables estimation of the underlying DAG for extremes using separation-based tests, and makes many state-of-the-art constraint-based causal discovery algorithms directly applicable. We further consider the problem of undirected graph estimation for relationships among tail-dependent (and potentially heavy-tailed) data. The effectiveness of our method, compared to alternative approaches, is validated through simulation studies on large-scale systems with up to 50 variables, and in a well-studied application to river discharge data from the Danube basin. Finally, we apply the framework to investigate complex market-wide relationships in China's derivatives market.