Counterfactual inference has become a ubiquitous tool in online advertisement, recommendation systems, medical diagnosis, and econometrics. Accurate modeling of outcome distributions associated with different interventions -- known as counterfactual distributions -- is crucial for the success of these applications. In this work, we propose to model counterfactual distributions using a novel Hilbert space representation called counterfactual mean embedding (CME). The CME embeds the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel, which allows us to perform causal inference over the entire landscape of the counterfactual distribution. Based on this representation, we propose a distributional treatment effect (DTE) that can quantify the causal effect over entire outcome distributions. Our approach is nonparametric as the CME can be estimated under the unconfoundedness assumption from observational data without requiring any parametric assumption about the underlying distributions. We also establish a rate of convergence of the proposed estimator which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Furthermore, our framework allows for more complex outcomes such as images, sequences, and graphs. Our experimental results on synthetic data and off-policy evaluation tasks demonstrate the advantages of the proposed estimator.
翻译:在网上广告、建议系统、医学诊断和计量经济学中,反事实推断已成为一个无处不在的工具。与不同干预措施(称为反事实分布)相关的结果分布的准确模型模型对于这些应用的成功至关重要。在这项工作中,我们提议使用名为反事实嵌入(CME)的Hilbert小说空间代表模式模拟反事实分布。CME将相关的反事实分布嵌入一个具有积极明确内核的再生产Hilbert空间(RKHS)中,这使我们能够对整个反事实分布的景观进行因果关系推断。基于这一表述,我们提议了一种分配处理效果(DTE),可以量化整个结果分布的因果关系。我们的方法是不相容的,因为根据观测数据没有根据的假设来估计CME,而不需要对基本分布作任何对应的假设。我们还确定了一个拟议估算师的趋同率,这取决于有条件平均值的平滑度和反事实分布图的全局。基于这个表达效果的Radion-imestimalalalal-imendimal imal-imalendimalalal-endal-ressalendal imal-viewal-viewdal-viewdal-viewdal-viewdal-viewdal-viewdal-viewdal-viewdal-viewdaldaldaldal-viewdaldaldaldaldaldaldaldaldaldaldaldal 。我们,让我们,让我们的模型,让我们,让我们,让我们的图像,让我们的图像的图像的排序。