Inferring Causal Direction from Observational Data: A Complexity Approach

TL;DR

This paper introduces simple, fast criteria based on complexity notions to infer causal direction between two variables from observational data, outperforming dependence tests alone.

Contribution

It proposes novel criteria leveraging complexity measures to distinguish cause from effect, applicable to discrete and continuous variables, with demonstrated high accuracy.

Findings

Criteria accurately infer causal direction on synthetic data

Different notions of simplicity improve causal inference

Criteria outperform traditional dependence tests

Abstract

At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using statistical dependence testing alone and requires that we make additional assumptions. We propose several fast and simple criteria for distinguishing cause and effect in pairs of discrete or continuous random variables. The intuition behind them is that predicting the effect variable using the cause variable should be `simpler' than the reverse -- different notions of `simplicity' giving rise to different criteria. We demonstrate the accuracy of the criteria on synthetic data generated under a broad family of causal mechanisms and types of noise.