Nonparametric Instrumental Variable Regression through Stochastic
  Approximate Gradients
Caio Peixoto Yuri Saporito Yuri Fonseca
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.