By taking into account the nonlinear effect of the cause, the inner noise effect, and the measurement distortion effect in the observed variables, the post-nonlinear (PNL) causal model has demonstrated its excellent performance in distinguishing the cause from effect. However, its identifiability has not been properly addressed, and how to apply it in the case of more than two variables is also a problem. In this paper, we conduct a systematic investigation on its identifiability in the two-variable case. We show that this model is identifiable in most cases; by enumerating all possible situations in which the model is not identifiable, we provide sufficient conditions for its identifiability. Simulations are given to support the theoretical results. Moreover, in the case of more than two variables, we show that the whole causal structure can be found by applying the PNL causal model to each structure in the Markov equivalent class and testing if the disturbance is independent of the direct causes for each variable. In this way the exhaustive search over all possible causal structures is avoided.

本研究通过系统研究二元情况下的可辨识性，证明了 PNL 因果模型在大多数情况下是可辨识的，同时为其可辨识性提供了充分条件。在多于两个变量的情况下，我们通过将 PNL 因果模型应用于 Markov 等价类中的每个结构，并测试干扰是否独立于直接原因确定整个因果结构，避免了对所有可能的因果结构进行穷举搜索。

关于后非线性因果模型的可识别性