Conditional average treatment effects (CATEs) allow us to understand the effect heterogeneity across a large population of individuals. However, typical CATE learners assume all confounding variables are measured in order for the CATE to be identifiable. This requirement can be satisfied by collecting many variables, at the expense of increased sample complexity for estimating CATEs. To combat this, we propose an energy-based model (EBM) that learns a low-dimensional representation of the variables by employing a noise contrastive loss function. With our EBM we introduce a preprocessing step that alleviates the dimensionality curse for any existing learner developed for estimating CATEs. We prove that our EBM keeps the representations partially identifiable up to some universal constant, as well as having universal approximation capability. These properties enable the representations to converge and keep the CATE estimates consistent. Experiments demonstrate the convergence of the representations, as well as show that estimating CATEs on our representations performs better than on the variables or the representations obtained through other dimensionality reduction methods.

翻译：有条件平均治疗效应(CATEs)使我们能够理解大量个人群体的影响异质性。然而,典型的CATE学习者认为,为了能够识别CATE,对所有令人困惑的变量都进行了测量。通过收集许多变量,可以满足这一要求,而牺牲了为估计CATE而增加的样本复杂性。为了解决这一问题,我们提议了一种基于能源的模式(EBM),通过使用噪音对比损失功能来了解变量的低维代表度。我们有了EBM,我们引入了一个预处理步骤,以缓解为估计CATE而开发的任何现有学习者的维度诅咒。我们证明,我们的EBM保持了部分可识别到某种普遍常数的表达方式,并且具有普遍近似能力。这些特性使CATE的表述能够趋同并保持CATE估算的一致性。实验表明,我们表述中的CATE比通过其他维度减少方法获得的变量或表述要好。