Learning Mixtures of Unknown Causal Interventions

TL;DR

This paper addresses the challenge of disentangling mixed interventional and observational data in linear SEMs with Gaussian noise, enabling causal discovery even with noisy intervention data.

Contribution

It introduces methods to recover causal structures from noisy mixed data without knowing the true causal graph, and establishes sample complexity bounds based on intervention effects.

Findings

Interventions provide sufficient diversity for causal component recovery.

Sample complexity inversely relates to intervention strength.

Causal graph can be identified up to interventional Markov equivalence.

Abstract

The ability to conduct interventions plays a pivotal role in learning causal relationships among variables, thus facilitating applications across diverse scientific disciplines such as genomics, economics, and machine learning. However, in many instances within these applications, the process of generating interventional data is subject to noise: rather than data being sampled directly from the intended interventional distribution, interventions often yield data sampled from a blend of both intended and unintended interventional distributions. We consider the fundamental challenge of disentangling mixed interventional and observational data within linear Structural Equation Models (SEMs) with Gaussian additive noise without the knowledge of the true causal graph. We demonstrate that conducting interventions, whether do or soft, yields distributions with sufficient diversity and properties conducive to efficiently recovering each component within the mixture. Furthermore, we establish that the sample complexity required to disentangle mixed data inversely correlates with the extent of change induced by an intervention in the equations governing the affected variable values. As a result, the causal graph can be identified up to its interventional Markov Equivalence Class, similar to scenarios where no noise influences the generation of interventional data. We further support our theoretical findings by conducting simulations wherein we perform causal discovery from such mixed data.