Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testing
This addresses a fundamental problem in causal discovery for researchers, but it is incremental as it compares existing methods under noise misspecification.
The paper tackles cause-effect inference in location-scale noise models, showing that maximum likelihood selection achieves state-of-the-art accuracy with correct noise specification but sharply deteriorates under misspecification, while residual independence testing is more robust.
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.