Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable flexible representations of complex relationships between variables. They serve as a mechanism for efficiently transferring the representation of a distribution downstream to other tasks, such as hypothesis testing or causal effect estimation. In the context of causal inference, the main challenges include identifying causal associations and estimating the average treatment effect from observational data, where confounding variables may obscure direct cause-and-effect relationships. Kernel embeddings provide a robust nonparametric framework for addressing these challenges. They allow for the representations of distributions of observational data and their seamless transformation into representations of interventional distributions to estimate relevant causal quantities. We overview recent research that leverages the expressiveness of kernel embeddings in tandem with causal inference.

翻译：核嵌入已成为在各类统计推断问题中表示概率测度的有力工具。通过将概率测度映射到再生核希尔伯特空间（RKHS），核嵌入能够灵活地表征变量间的复杂关系。它们作为一种机制，可将分布表示高效迁移至下游任务，如假设检验或因果效应估计。在因果推断领域，主要挑战包括从观测数据中识别因果关联与估计平均处理效应，其中混杂变量可能掩盖直接的因果关系。核嵌入为解决这些挑战提供了一个稳健的非参数框架。该框架支持对观测数据分布进行表征，并将其无缝转化为干预分布的表示，从而估计相关因果量。本文综述了近期结合核嵌入的表达能力与因果推断的研究进展。