我们解决了在没有观察到的混杂的存在下的因果效应估计的问题，但是观察到潜在混杂因素的代理。在这种情况下，我们提出了两种基于内核的方法，用于非线性因果效应估计：（a）两阶段回归方法，以及（b）最大矩限制方法。我们专注于近端因果学习设置，但是我们的方法可以用来解决以弗雷霍尔姆积分方程为特征的更广泛的逆问题。特别是，我们提供了在非线性环境中解决此问题的两阶段和矩限制方法的统一视图。我们为每种算法提供一致性保证，并证明这些方法在合成数据和模拟现实世界任务的数据上获得竞争结果。特别是，我们的方法优于不适合利用代理变量的早期方法。

Maternal and child mortality is a public health problem that disproportionately affects low-and middle-income countries. Every day, 800 women and 6,700 newborns die from complications related to pregnancy or childbirth. And for every maternal death, about 20 women suffer serious birth injuries. However, nearly all of these deaths and negative health outcomes are preventable. Midwives are key to revert this situation, and thus it is essential to strengthen their capacities and the quality of their education. This is the aim of the Safe Delivery App, a digital job aid and learning tool to enhance the knowledge, confidence and skills of health practitioners. Here, we use the behavioral logs of the App to implement a recommendation system that presents each midwife with suitable contents to continue gaining expertise. We focus on predicting the click-through rate, the probability that a given user will click on a recommended content. We evaluate four deep learning models and show that all of them produce highly accurate predictions.