On the role of additive regression for (high-dimensional) causal inference
Jan Ernest, Peter Bühlmann · arXiv (Cornell University) · 2014
Abstract: We consider the problem of inferring the (total) causal effect of a single variable intervention on a (response) variable of interest. We prove that for a very general class of structural equation models with known or-der of the variables, it is sufficient to use additive regression, even for cases where the structural equation model has non-additive functional form: we call the procedure ord-additive regression. As such, our result implies a major robustness property with respect to model misspecification. Further-more, when the order of the variables is not known, we can estimate (the equivalence class of) the order of the variables, or (the equivalence class of) the directed acyclic graph corresponding to the structural equation model, and then proceed by using these estimates as a substitute for the true quantities. We empirically compare the ord-additive regression method with more classical approaches and argue that the former is indeed more robust, reliable and much simpler. 1.