Unobserved confounding is one of the main challenges when estimating causal effects. We propose a causal reduction method that, given a causal model, replaces an arbitrary number of possibly high-dimensional latent confounders with a single latent confounder that takes values in the same space as the treatment variable, without changing the observational and interventional distributions the causal model entails. This allows us to estimate the causal effect in a principled way from combined data without relying on the common but often unrealistic assumption that all confounders have been observed. We apply our causal reduction in three different settings. In the first setting, we assume the treatment and outcome to be discrete. The causal reduction then implies bounds between the observational and interventional distributions that can be exploited for estimation purposes. In certain cases with highly unbalanced observational samples, the accuracy of the causal effect estimate can be improved by incorporating observational data. Second, for continuous variables and assuming a linear-Gaussian model, we derive equality constraints for the parameters of the observational and interventional distributions. Third, for the general continuous setting (possibly nonlinear and non-Gaussian), we parameterize the reduced causal model using normalizing flows, a flexible class of easily invertible nonlinear transformations. We perform a series of experiments on synthetic data and find that in several cases the number of interventional samples can be reduced when adding observational training samples without sacrificing accuracy.
翻译:在估计因果关系时,我们提出了一种因果减少方法,根据一个因果模型,用一个与治疗变量在同一空间、不改变因果模型所伴随的观察和干预分布的单一潜伏混淆器,取代任意数量的可能高维潜伏沉积器,将数值与处理变量在同一空间,而不改变因果模型所伴随的观察和干预分布。这使我们能够从综合数据中以原则性方式估计因果关系,而不必依赖观察到所有混淆者的常见但往往不切实际的假设。我们在三个不同的环境中应用我们的因果减少。在第一个环境中,我们假定治疗和结果是分立的。因此,因果减少意味着可以用于估算目的的观测和干预分布之间的界限。在某些情况下,如果观测样本高度不平衡,则可以通过纳入观测数据来改进因果估计的准确性。第二,对于连续变量和假设线性-冈比亚模型,我们可以从观察和干预分布参数中得出平等性限制。第三,对于一般连续设置(在不精确性观测样本中可能非线性和非伽西值的精确性),因此,我们用一个正常的、不易变的模型来测量性模型来测量。