The need for modelling causal knowledge at different levels of granularity arises in several settings. Causal Abstraction provides a framework for formalizing this problem by relating two Structural Causal Models at different levels of detail. Despite increasing interest in applying causal abstraction, e.g. in the interpretability of large machine learning models, the graphical and parametrical conditions under which a causal model can abstract another are not known. Furthermore, learning causal abstractions from data is still an open problem. In this work, we tackle both issues for linear causal models with linear abstraction functions. First, we characterize how the low-level coefficients and the abstraction function determine the high-level coefficients and how the high-level model constrains the causal ordering of low-level variables. Then, we apply our theoretical results to learn high-level and low-level causal models and their abstraction function from observational data. In particular, we introduce Abs-LiNGAM, a method that leverages the constraints induced by the learned high-level model and the abstraction function to speedup the recovery of the larger low-level model, under the assumption of non-Gaussian noise terms. In simulated settings, we show the effectiveness of learning causal abstractions from data and the potential of our method in improving scalability of causal discovery.

采用线性因果模型的线性抽象函数，本研究首先确定了低级系数和抽象函数如何决定高级系数，以及高级模型如何约束低级变量的因果顺序；然后，通过观测数据学习了高级和低级因果模型及其抽象函数，并提出了一种名为Abs-LiNGAM的方法，利用所学高级模型和抽象函数所引导的约束，加快了更大规模低级模型的恢复过程，假设产生噪声项为非高斯分布；通过模拟实验验证了从数据中学习因果抽象的有效性以及我们的方法在改善因果发现的可扩展性方面的潜力。

线性结构因果模型的因果抽象学习