One fundamental problem in causal inference is the treatment effect estimation in observational studies, and its key challenge is to handle the confounding bias induced by the associations between covariates and treatment variable. In this paper, we study the problem of effect estimation on continuous treatment from observational data, going beyond previous work on binary treatments. Previous work on binary treatment focuses on de-confounding by balancing the distribution of covariates between the treated and control groups with either propensity score or confounder balancing techniques. In the continuous setting, those methods would fail as we can hardly evaluate the distribution of covariates under each treatment status. To tackle the case of continuous treatments, we propose a novel Generative Adversarial De-confounding (GAD) algorithm to eliminate the associations between covariates and treatment variable with two main steps: (1) generating an “calibration” distribution without associations between covariates and treatment by randomly perturbation on treatment variable; (2) learning sample weights that transfer the distribution of observed data to the “calibration” distribution for de-confounding with a Generative Adversarial Network. We show, both theoretically and with empirical experiments, that our GAD algorithm can remove the associations between covariates and treatment, hence, precisely estimating the causal effect of continuous treatment. Extensive experiments on both synthetic and real-world datasets demonstrate that our algorithm outperforms the state-of-the-art methods for effect estimation of continuous treatment with observational data.

因果推断的一个基本问题是观察性研究中的治疗效果估计，其关键挑战是处理由协变量和治疗变量之间的关联引起的混杂偏差。在本文中，我们研究了从观察数据对连续处理的效果估计问题，超越了以前关于二元处理的工作。先前关于二元处理的工作侧重于通过使用倾向评分或混杂因素平衡技术平衡处理组和对照组之间的协变量分布来消除混杂。在连续设置中，这些方法将失败，因为我们几乎无法评估每种处理状态下协变量的分布。为了解决连续治疗的情况，我们提出了一种新的生成对抗性去混淆 (GAD) 算法，通过两个主要步骤来消除协变量和治疗变量之间的关联：(1) 通过对治疗变量的随机扰动，生成协变量和治疗之间没有关联的“校准”分布；(2) 学习样本权重，将观测数据的分布转移到“校准”分布，以与生成对抗网络去混淆。我们通过理论和经验实验表明，我们的 GAD 算法可以消除协变量和治疗之间的关联，因此，可以精确估计连续治疗的因果效应。