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：本文针对存在隐混杂因子的因果效应估计问题展开研究，重点关注两种设定：包含额外观测混杂变量的工具变量回归，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，继而构建鞍点优化问题。在工具变量回归的语境下，该方法可视为Darolles等人[2011]开创性方法的神经网络推广。鞍点优化框架近期受到广泛关注，因其能够避免双重采样偏差，并适用于现代函数逼近方法。我们在多种实验设定下进行了验证，结果表明该方法在常用基准测试中优于现有方法。