The abilities of humans to understand the world in terms of cause and effect relationships, as well as to compress information into abstract concepts, are two hallmark features of human intelligence. These two topics have been studied in tandem in the literature under the rubric of causal abstractions theory. In practice, it remains an open problem how to best leverage abstraction theory in real-world causal inference tasks, where the true mechanisms are unknown and only limited data is available. In this paper, we develop a new family of causal abstractions by clustering variables and their domains. This approach refines and generalizes previous notions of abstractions to better accommodate individual causal distributions that are spawned by Pearl's causal hierarchy. We show that such abstractions are learnable in practical settings through Neural Causal Models (Xia et al., 2021), enabling the use of the deep learning toolkit to solve various challenging causal inference tasks -- identification, estimation, sampling -- at different levels of granularity. Finally, we integrate these results with representation learning to create more flexible abstractions, moving these results closer to practical applications. Our experiments support the theory and illustrate how to scale causal inferences to high-dimensional settings involving image data.

翻译：人类通过因果关系理解世界以及将信息压缩为抽象概念的能力，是智能的两个标志性特征。这两个主题在文献中已通过因果抽象理论框架得到并行研究。然而在实际应用中，如何最佳利用抽象理论解决真实世界因果推断任务（其中真实机制未知且仅有有限数据可用）仍是一个开放问题。本文通过聚类变量及其域，发展了一类新的因果抽象方法。该方法改进并推广了先前的抽象概念，使其能更好地适应Pearl因果层级中产生的个体因果分布。我们证明这类抽象在实践场景中可通过神经因果模型（Xia等，2021）学习，从而利用深度学习工具集解决不同粒度层面上的多个具有挑战性的因果推断任务——识别、估计、采样。最后，我们将这些结果与表征学习相整合，创建更灵活的抽象方法，使相关成果更接近实际应用。我们的实验支持该理论，并展示了如何将因果推断扩展至涉及图像数据的高维场景。