We consider the estimation of average and counterfactual treatment effects, under two settings: back-door adjustment and front-door adjustment. The goal in both cases is to recover the treatment effect without having an access to a hidden confounder. This objective is attained by first estimating the conditional mean of the desired outcome variable given relevant covariates (the "first stage" regression), and then taking the (conditional) expectation of this function as a "second stage" procedure. We propose to compute these conditional expectations directly using a regression function to the learned input features of the first stage, thus avoiding the need for sampling or density estimation. All functions and features (and in particular, the output features in the second stage) are neural networks learned adaptively from data, with the sole requirement that the final layer of the first stage should be linear. The proposed method is shown to converge to the true causal parameter, and outperforms the recent state-of-the-art methods on challenging causal benchmarks, including settings involving high-dimensional image data.
翻译:在两种情况下,我们考虑对平均和反实际治疗效果的估计:后门调整和前门调整。两种情况下的目标是恢复治疗效果,而不必接触隐蔽的混乱者。实现这一目标的方法是首先根据相关的共变(“第一阶段”回归)估计预期结果变量的有条件值,然后将这一函数的(有条件)预期作为“第二阶段”程序。我们提议利用一个回归函数直接计算这些有条件的预期值到第一阶段的学习输入特征,从而避免取样或密度估计的需要。所有功能和特征(特别是第二阶段的输出特征)都是从数据中适应性地学习的神经网络,唯一的要求第一阶段的最后一层应当是线性。拟议方法显示与真正的因果参数趋同,并超越了挑战性因果基准的最近最先进的方法,包括涉及高维图像数据的环境。