Assessing the overall and partial causal well-specification of nonlinear additive noise models

Nonlinear additive noise models and their heteroscedastic extensions are a popular modelling framework for causal discovery and inference. They allow to infer the true causal connections and effects from the multivariate distribution when the nonparametric model is correct; see, e.g., Hoyer et al. (2008); Peters et al. (2014) or, for heteroscedastic models, Strobl and Lasko (2023); Immer et al. (2023). However, the conclusions can be misleading if the additive noise model is misspecified, especially in the presence of hidden confounding variables. In this paper, we define the term "causal well-specification" of additive noise models, discuss its relevance, and finally present a corresponding estimation technique for observational data. The concept of well-specification for regression functionals in parametric regression was introduced by Buja et al. (2019).