Nonparametric Instrumental Variable Regression through Stochastic Approximate Gradients

This paper proposes SAGD-IV, a novel framework for conducting nonparametric instrumental variable (NPIV) regression by employing stochastic approximate gradients to minimize the projected populational risk. Instrumental Variables (IVs) are widely used in econometrics to address estimation problems in the presence of unobservable confounders, and the Machine Learning community has devoted significant effort to improving existing methods and devising new ones in the NPIV setting, which is known to be an ill-posed linear inverse problem. We provide theoretical support for our algorithm and further exemplify its competitive performance through empirical experiments. Furthermore, we address, with promising results, the case of binary outcomes, which has not received as much attention from the community as its continuous counterpart.