On Causal Discovery with Equal Variance Assumption

TL;DR

This paper introduces a new causal discovery method based on ordering conditional variances, which simplifies structure learning and extends to high-dimensional data, building on the equal variance assumption.

Contribution

It reveals that causal structure can be identified through variance ordering and proposes a state-of-the-art, scalable method for high-dimensional causal discovery.

Findings

Variance ordering implies causal structure identification.

The proposed method achieves state-of-the-art performance.

Method extends to high-dimensional causal discovery.

Abstract

Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among (conditional) variances. We demonstrate that ordering estimates of these variances yields a simple yet state-of-the-art method for causal structure learning that is readily extendable to high-dimensional problems.