Nonparametric Instrumental Variable Regression through Stochastic Approximate Gradients

Resumo

Causal inference from observational data presents unique challenges, primarily due to the potential for confounding variables that can affect both outcomes and covariates of interest. When unobservable confounders exist, approaches that rely on instrumental variables (IVs) — quantities that are correlated with the variable of interest (relevance condition) and are independent of the unobservable confounders — offer a way to still identify causal effects. In this work, we present a novel framework for nonparametric IV (NPIV) estimation that relies on stochastic approximate gradients and demonstrate finite sample bounds for the projected populational risk of our estimator. The challenge is that NPIV estimation, although more capable of adapting to the intrinsic structure of the data when compared to its parametric counterpart, is an ill-posed inverse problem.