On the pitfalls of Gaussian likelihood scoring for causal discovery

TL;DR

This paper investigates the limitations of using Gaussian likelihood scores for causal discovery, revealing that such methods can fail under model misspecification, especially with non-Gaussian errors.

Contribution

The paper provides a theoretical analysis showing the failure modes of Gaussian likelihood scoring in causal discovery when errors are non-Gaussian.

Findings

Gaussian likelihood scoring can be inconsistent with non-Gaussian errors

Model misspecification leads to incorrect causal inferences

Nonparametric regression does not mitigate Gaussian score pitfalls

Abstract

We consider likelihood score-based methods for causal discovery in structural causal models. In particular, we focus on Gaussian scoring and analyze the effect of model misspecification in terms of non-Gaussian error distribution. We present a surprising negative result for Gaussian likelihood scoring in combination with nonparametric regression methods.