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.

本文提出了 SAGD-IV, 一种新颖的非参数工具变量回归框架，通过使用随机近似梯度来最小化投影总体风险。我们在理论上支持了算法，并通过实证实验证明了它的竞争性能。此外，我们也着重研究了二元结果的情况并取得了有希望的结果。

非参数工具变量回归通过随机近似梯度

Nonparametric Instrumental Variable Regression through Stochastic  Approximate Gradients

Instrumental variables (IVs) are widely used for estimating causal effects in
the presence of unmeasured confounding. Under the standard IV model, however,
the average treatment effect (ATE) is only partially identifiable. To address
this, we propose novel assumptions that allow for identification of the ATE.
Our identification assumptions are clearly separated from model assumptions
needed for estimation, so that researchers are not required to commit to a
specific observed data model in establishing identification. We then construct
multiple estimators that are consistent under three different observed data
models, and multiply robust estimators that are consistent in the union of
these observed data models. We pay special attention to the case of binary
outcomes, for which we obtain bounded estimators of the ATE that are guaranteed
to lie between -1 and 1. Our approaches are illustrated with simulations and a
data analysis evaluating the causal effect of education on earnings.

本文提出了新的假设条件，允许在标准 IV 模型下识别平均处理效应（ATE），并构建了多个估计器，这些估计器在三个不同的观察数据模型下是一致的，并设计保证 ATE 估计值在 - 1 到 1 之间的估计器。