Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testing

TL;DR

This paper compares maximum likelihood and independence testing methods for cause-effect inference in location-scale noise models, highlighting robustness issues with likelihood under noise misspecification and proposing residual independence testing as a more reliable alternative.

Contribution

It provides an empirical evaluation of likelihood-based model selection versus independence testing in cause-effect inference, revealing the latter's robustness to noise misspecification.

Findings

Likelihood-based model selection deteriorates with noise misspecification.

Residual independence testing is more robust to noise distribution errors.

Conditional variance differences influence model selection accuracy.

Abstract

A fundamental problem of causal discovery is cause-effect inference, learning the correct causal direction between two random variables. Significant progress has been made through modelling the effect as a function of its cause and a noise term, which allows us to leverage assumptions about the generating function class. The recently introduced heteroscedastic location-scale noise functional models (LSNMs) combine expressive power with identifiability guarantees. LSNM model selection based on maximizing likelihood achieves state-of-the-art accuracy, when the noise distributions are correctly specified. However, through an extensive empirical evaluation, we demonstrate that the accuracy deteriorates sharply when the form of the noise distribution is misspecified by the user. Our analysis shows that the failure occurs mainly when the conditional variance in the anti-causal direction is smaller than that in the causal direction. As an alternative, we find that causal model selection through residual independence testing is much more robust to noise misspecification and misleading conditional variance.