  We consider the problem of inferring the total causal effect of a single
variable intervention on a (response) variable of interest. We propose a
certain marginal integration regression technique for a very general class of
potentially nonlinear structural equation models (SEMs) with known structure,
or at least known superset of adjustment variables: we call the procedure
S-mint regression. We easily derive that it achieves the convergence rate as
for nonparametric regression: for example, single variable intervention effects
can be estimated with convergence rate $n^{-2/5}$ assuming smoothness with
twice differentiable functions. Our result can also be seen as a major
robustness property with respect to model misspecification which goes much
beyond the notion of double robustness. Furthermore, when the structure of the
SEM is not known, we can estimate (the equivalence class of) the directed
acyclic graph corresponding to the SEM, and then proceed by using S-mint based
on these estimates. We empirically compare the S-mint regression method with
more classical approaches and argue that the former is indeed more robust, more
reliable and substantially simpler.
