Causal representation learning seeks to uncover latent, high-level causal representations from low-level observed data. It is particularly good at predictions under unseen distribution shifts, because these shifts can generally be interpreted as consequences of interventions. Hence leveraging {seen} distribution shifts becomes a natural strategy to help identifying causal representations, which in turn benefits predictions where distributions are previously {unseen}. Determining the types (or conditions) of such distribution shifts that do contribute to the identifiability of causal representations is critical. This work establishes a {sufficient} and {necessary} condition characterizing the types of distribution shifts for identifiability in the context of latent additive noise models. Furthermore, we present partial identifiability results when only a portion of distribution shifts meets the condition. In addition, we extend our findings to latent post-nonlinear causal models. We translate our findings into a practical algorithm, allowing for the acquisition of reliable latent causal representations. Our algorithm, guided by our underlying theory, has demonstrated outstanding performance across a diverse range of synthetic and real-world datasets. The empirical observations align closely with the theoretical findings, affirming the robustness and effectiveness of our approach.

翻译：因果表征学习旨在从低层观测数据中挖掘潜在的高层因果表征。该方法在处理未见分布偏移下的预测任务时尤为有效，因为这类偏移通常可解释为干预的结果。因此，利用{已见}分布偏移成为识别因果表征的自然策略，这反过来又有助于对{未见}分布偏移场景的预测。明确哪些类型（或条件）的分布偏移能真正促进因果表征的可识别性至关重要。本研究针对潜在加性噪声模型，建立了刻画分布偏移类型对于可识别性的{充分必要条件}。进一步地，当仅部分分布偏移满足该条件时，我们给出了部分可识别性结论。此外，还将研究结论拓展至潜在后非线性因果模型。我们将理论发现转化为实用算法，实现了可靠潜在因果表征的获取。该算法在理论指导下，已在多种合成和真实世界数据集上展现出卓越性能。实验观测与理论发现高度吻合，验证了方法的鲁棒性和有效性。