We address the problem of causal effect estimation in the presence of unobserved confounding, but where proxies for the latent confounder(s) are observed. We propose two kernel-based methods for nonlinear causal effect estimation in this setting: (a) a two-stage regression approach, and (b) a maximum moment restriction approach. We focus on the proximal causal learning setting, but our methods can be used to solve a wider class of inverse problems characterised by a Fredholm integral equation. In particular, we provide a unifying view of two-stage and moment restriction approaches for solving this problem in a nonlinear setting. We provide consistency guarantees for each algorithm, and we demonstrate these approaches achieve competitive results on synthetic data and data simulating a real-world task. In particular, our approach outperforms earlier methods that are not suited to leveraging proxy variables.
翻译:在未观察到的混乱情况下,我们解决因果估计问题,但观察的是潜在困惑者的代理人。我们在此背景下提出了两种基于内核的非线性因果估计方法:(a) 双阶段回归法,和(b) 最大时间限制法。我们侧重于准因果学习环境,但我们的方法可以用来解决以Fredholm整体方程式为特征的更广泛的反向问题。特别是,我们对在非线性环境下解决这一问题的两阶段和瞬间限制方法提供了统一的观点。我们为每种算法提供了一致性保证,我们展示了这些方法在合成数据和模拟现实世界任务的数据上取得了竞争性结果。特别是,我们的方法优于早先不适于利用替代变量的方法。