Causal Discovery with Continuous Additive Noise Models

TL;DR

This paper demonstrates that causal directed acyclic graphs can be uniquely identified from observational data when the data follow a structural equation model with additive noise, offering a new approach to causal discovery.

Contribution

It introduces the concept that additive noise models enable identifiability of causal graphs from observational data, unlike traditional methods that only recover equivalence classes.

Findings

RESIT algorithm is correct in the population setting

Additive noise models allow full causal graph identifiability

Empirical evaluation supports the proposed methods

Abstract

We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show that if the observational distribution follows a structural equation model with an additive noise structure, the directed acyclic graph becomes identifiable from the distribution under mild conditions. This constitutes an interesting alternative to traditional methods that assume faithfulness and identify only the Markov equivalence class of the graph, thus leaving some edges undirected. We provide practical algorithms for finitely many samples, RESIT (Regression with Subsequent Independence Test) and two methods based on an independence score. We prove that RESIT is correct in the population setting and provide an empirical evaluation.