Instrumental variables (IVs) provide a powerful strategy for identifying causal effects in the presence of unobservable confounders. Within the nonparametric setting (NPIV), recent methods have been based on nonlinear generalizations of Two-Stage Least Squares and on minimax formulations derived from moment conditions or duality. In a novel direction, we show how to formulate a functional stochastic gradient descent algorithm to tackle NPIV regression by directly minimizing the populational risk. We provide theoretical support in the form of bounds on the excess risk, and conduct numerical experiments showcasing our method's superior stability and competitive performance relative to current state-of-the-art alternatives. This algorithm enables flexible estimator choices, such as neural networks or kernel based methods, as well as non-quadratic loss functions, which may be suitable for structural equations beyond the setting of continuous outcomes and additive noise. Finally, we demonstrate this flexibility of our framework by presenting how it naturally addresses the important case of binary outcomes, which has received far less attention by recent developments in the NPIV literature.

翻译：工具变量（IVs）为存在不可观测混杂因素时的因果效应识别提供了强有力的策略。在非参数设定（NPIV）下，近期方法主要基于两阶段最小二乘法的非线性推广，以及从矩条件或对偶性导出的极小极大化表述。本文提出一种新颖思路：通过直接最小化总体风险，构建函数型随机梯度下降算法以解决NPIV回归问题。我们从理论层面提供了超额风险的界作为支撑，并通过数值实验证明，相较于当前最先进的替代方法，本算法具有更优的稳定性与具有竞争力的性能。该算法支持灵活的估计器选择（如神经网络或基于核的方法）以及非二次损失函数，适用于连续结果与加性噪声设定之外的结构方程建模。最后，我们通过展示该框架如何自然处理二元结果这一重要案例（该案例在近期NPIV文献中较少受到关注），证明了本方法的灵活性。