We address the problem of causal effect estimation where hidden confounders are present, with a focus on two settings: instrumental variable regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator, followed by a saddle-point optimization problem, which, in the context of IV regression, can be thought of as a neural net generalization of the seminal approach due to Darolles et al. [2011]. Saddle-point formulations have gathered considerable attention recently, as they can avoid double sampling bias and are amenable to modern function approximation methods. We provide experimental validation in various settings, and show that our approach outperforms existing methods on common benchmarks.

翻译：我们研究了存在隐混杂因子情况下的因果效应估计问题，重点关注两种设定：包含额外观测混杂因子的工具变量回归，以及代理因果学习。我们的方法通过对条件期望算子进行奇异值分解，随后求解鞍点优化问题来实现。在工具变量回归的背景下，该方法可视为Darolles等人[2011]开创性方法的神经网络推广。鞍点优化公式近年来受到广泛关注，因其能够避免双重抽样偏差，且适用于现代函数逼近方法。我们在多种设定下进行了实验验证，结果表明该方法在常见基准测试中优于现有方法。