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

Location-scale noise models (LSNMs) are a class of heteroscedastic structural causal models with wide applicability, closely related to affine flow models. Recent likelihood-based methods designed for LSNMs that infer cause-effect relationships achieve state-of-the-art accuracy, when their assumptions are satisfied concerning the noise distributions. However, under misspecification their accuracy deteriorates sharply, especially when the conditional variance in the anti-causal direction is smaller than that in the causal direction. In this paper, we demonstrate the misspecification problem and analyze why and when it occurs. We show that residual independence testing is much more robust to misspecification than likelihood-based cause-effect inference. Our empirical evaluation includes 580 synthetic and 99 real-world datasets.