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.

翻译：本文提出SAGD-IV框架，一种通过采用随机近似梯度最小化投影总体风险的新型非参数工具变量（NPIV）回归方法。工具变量（IVs）在计量经济学中被广泛用于解决存在不可观测混淆变量时的估计问题，机器学习社区一直致力于改进现有方法并设计NPIV场景下的新方法——该场景被公认为不适定线性逆问题。我们为所提算法提供了理论支撑，并通过实证实验进一步验证了其竞争性性能。此外，针对二值输出这一较连续输出而言未获学术界足够关注的场景，我们以富有前景的成果进行了处理。