We investigate nonlinear instrumental variable (IV) regression given high-dimensional instruments. We propose a simple algorithm which combines kernelized IV methods and an arbitrary, adaptive regression algorithm, accessed as a black box. Our algorithm enjoys faster-rate convergence and adapts to the dimensionality of informative latent features, while avoiding an expensive minimax optimization procedure, which has been necessary to establish similar guarantees. It further brings the benefit of flexible machine learning models to quasi-Bayesian uncertainty quantification, likelihood-based model selection, and model averaging. Simulation studies demonstrate the competitive performance of our method.

翻译：我们调查了非线性工具变量(IV)回归给高维仪器。我们提出了一个简单的算法,将内嵌四型方法和任意的、适应性回归算法结合起来,作为黑匣子使用。我们的算法具有更快的趋同率,并适应了信息化潜在特征的维度,同时避免了昂贵的小型最大优化程序,这是建立类似保障所必须的。它进一步将灵活的机器学习模型的好处带给准贝耶斯的不确定性量化、基于可能性的模型选择和平均模型。模拟研究显示了我们方法的竞争性性能。