Unobserved confounding is one of the main challenges when estimating causal effects. We propose a novel causal reduction method that replaces an arbitrary number of possibly high-dimensional latent confounders with a single latent confounder that lives in the same space as the treatment variable without changing the observational and interventional distributions entailed by the causal model. After the reduction, we parameterize the reduced causal model using a flexible class of transformations, so-called normalizing flows. We propose a learning algorithm to estimate the parameterized reduced model jointly from observational and interventional data. This allows us to estimate the causal effect in a principled way from combined data. We perform a series of experiments on data simulated using nonlinear causal mechanisms and find that we can often substantially reduce the number of interventional samples when adding observational training samples without sacrificing accuracy. Thus, adding observational data may help to more accurately estimate causal effects even in the presence of unobserved confounders.
翻译:在估计因果关系时,未观察到的混乱是主要挑战之一。 我们提出一种新的因果减少方法, 取代任意数量的可能高维潜伏混淆器, 替换任意数量的可能高维潜伏混淆器, 代之以一个单一的潜伏混淆器, 与处理变量居住在同一个空间, 而不改变因果模型引起的观察和干预分布。 在减少后, 我们使用灵活的变异类别, 即所谓的正常流, 将减少的因果模型参数化参数化为参数化。 我们提出一种学习算法, 用观察和干预数据来估计参数化的减值模型。 这使我们能够从综合数据中以有原则的方式估计因果关系。 我们用非线性因果机制模拟的数据进行了一系列实验, 发现在不牺牲准确性的情况下添加观察训练样本时, 我们往往可以大量减少干预样本的数量。 因此, 添加观察数据也许有助于更准确地估计因果关系, 即使存在未观察到的同流体, 。