Telling cause from effect based on high-dimensional observations

TL;DR

This paper introduces a method for inferring causal directions between high-dimensional variables by exploiting distributional asymmetries, effective for both stochastic and deterministic relations in high-dimensional data.

Contribution

The paper presents a novel approach leveraging distribution asymmetries to determine causality in high-dimensional settings, applicable to Gaussian and non-Gaussian data.

Findings

Works with both stochastic and deterministic causal relations

Effective in high-dimensional scenarios, even with as few as 5 dimensions

Applicable to Gaussian and non-Gaussian data

Abstract

We describe a method for inferring linear causal relations among multi-dimensional variables. The idea is to use an asymmetry between the distributions of cause and effect that occurs if both the covariance matrix of the cause and the structure matrix mapping cause to the effect are independently chosen. The method works for both stochastic and deterministic causal relations, provided that the dimensionality is sufficiently high (in some experiments, 5 was enough). It is applicable to Gaussian as well as non-Gaussian data.