We consider inferring the causal effect of a treatment (intervention) on an outcome of interest in situations where there is potentially an unobserved confounder influencing both the treatment and the outcome. This is achievable by assuming access to two separate sets of control (proxy) measurements associated with treatment and outcomes, which are used to estimate treatment effects through a function termed the em causal bridge (CB). We present a new theoretical perspective, associated assumptions for when estimating treatment effects with the CB is feasible, and a bound on the average error of the treatment effect when the CB assumptions are violated. From this new perspective, we then demonstrate how coupling the CB with an autoencoder architecture allows for the sharing of statistical strength between observed quantities (proxies, treatment, and outcomes), thus improving the quality of the CB estimates. Experiments on synthetic and real-world data demonstrate the effectiveness of the proposed approach in relation to the state-of-the-art methodology for proxy measurements.

翻译：本文研究在存在潜在未观测混杂因子同时影响处理变量与结果变量的情况下，推断处理（干预）对目标结果的因果效应。该问题可通过假设存在分别与处理变量和结果变量相关联的两组独立控制（代理）测量值来实现，这些测量值通过称为因果桥的函数用于估计处理效应。我们提出新的理论视角、基于因果桥估计处理效应可行的相关假设，以及因果桥假设被违反时处理效应平均误差的界。基于这一新视角，我们进一步论证如何通过将因果桥与自编码器架构耦合，实现观测变量（代理变量、处理变量与结果变量）间统计强度的共享，从而提升因果桥估计量的质量。在合成数据与真实数据上的实验表明，所提方法相较于代理测量领域的最先进方法具有显著优势。