Discovering causal relations from observational data is important. The existence of unobserved variables (e.g. latent confounding or mediation) can mislead the causal identification. To overcome this problem, proximal causal discovery methods attempted to adjust for the bias via the proxy of the unobserved variable. Particularly, hypothesis test-based methods proposed to identify the causal edge by testing the induced violation of linearity. However, these methods only apply to discrete data with strict level constraints, which limits their practice in the real world. In this paper, we fix this problem by extending the proximal hypothesis test to cases where the system consists of continuous variables. Our strategy is to present regularity conditions on the conditional distributions of the observed variables given the hidden factor, such that if we discretize its observed proxy with sufficiently fine, finite bins, the involved discretization error can be effectively controlled. Based on this, we can convert the problem of testing continuous causal relations to that of testing discrete causal relations in each bin, which can be effectively solved with existing methods. These non-parametric regularities we present are mild and can be satisfied by a wide range of structural causal models. Using both simulated and real-world data, we show the effectiveness of our method in recovering causal relations when unobserved variables exist.

本文介绍了一种在存在连续变量的情况下发现因果关系的方法，通过解决离散数据的严格级别约束限制的问题，把连续因果关系测试转换为每个区间内离散因果关系的测试, 这些非参数规则可以广泛适用于大量结构因果模型。

利用代理变量方法进行未观测变量的因果发现