In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and thus can be recovered using autoregressive normalizing flows (NFs). Second, we analyze different design and learning choices for causal normalizing flows to capture the underlying causal data-generating process. Third, we describe how to implement the do-operator in causal NFs, and thus, how to answer interventional and counterfactual questions. Finally, in our experiments, we validate our design and training choices through a comprehensive ablation study; compare causal NFs to other approaches for approximating causal models; and empirically demonstrate that causal NFs can be used to address real-world problems, where the presence of mixed discrete-continuous data and partial knowledge on the causal graph is the norm. The code for this work can be found at https://github.com/psanch21/causal-flows.

翻译：在这项工作中，我们深入探讨了归一化流在因果推理中的应用。具体而言，我们首先利用非线性独立成分分析的最新成果，证明在给定因果顺序的情况下，因果模型可从观测数据中识别，因此可通过自回归归一化流进行恢复。其次，我们分析了因果归一化流在捕获底层因果数据生成过程中的不同设计与学习选择。第三，我们描述了如何在因果归一化流中实现do算子，从而解答干预和反事实问题。最后，在实验中，我们通过全面的消融研究验证了设计与训练选择；将因果归一化流与其他近似因果模型的方法进行比较；并实证证明因果归一化流可用于解决实际问题，其中混合离散-连续数据及因果图的部分知识是常态。本研究的代码可在https://github.com/psanch21/causal-flows获取。