Causal representation learning aims to unveil latent high-level causal
representations from observed low-level data. One of its primary tasks is to
provide reliable assurance of identifying these latent causal models, known as
identifiability. A recent breakthrough explores identifiability by leveraging
the change of causal influences among latent causal variables across multiple
environments \citep{liu2022identifying}. However, this progress rests on the
assumption that the causal relationships among latent causal variables adhere
strictly to linear Gaussian models. In this paper, we extend the scope of
latent causal models to involve nonlinear causal relationships, represented by
polynomial models, and general noise distributions conforming to the
exponential family. Additionally, we investigate the necessity of imposing
changes on all causal parameters and present partial identifiability results
when part of them remains unchanged. Further, we propose a novel empirical
estimation method, grounded in our theoretical finding, that enables learning
consistent latent causal representations. Our experimental results, obtained
from both synthetic and real-world data, validate our theoretical contributions
concerning identifiability and consistency.

从观察到的低级数据中揭示潜在高级因果表征是因果表征学习的目标之一，本文通过对多个环境中潜在因果变量之间因果影响的变化进行识别性探索，扩展了潜在因果模型的范围以涉及非线性因果关系，并且提出了一种新的经验估计方法，通过理论发现为学习一致的潜在因果表征提供了可行性。