Marginal integration for nonparametric causal inference

TL;DR

This paper introduces S-mint regression, a nonparametric method for estimating causal effects in complex models, demonstrating robustness, convergence rates, and applicability even with unknown structures.

Contribution

The paper proposes S-mint regression, a novel nonparametric causal inference technique that is robust, achieves optimal convergence rates, and can handle unknown model structures.

Findings

S-mint achieves $n^{-2/5}$ convergence rate for intervention effects.

S-mint is more robust and reliable than classical methods.

The method works with estimated SEM structures when the true structure is unknown.

Abstract

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.