In unsupervised causal representation learning for sequential data with
time-delayed latent causal influences, strong identifiability results for the
disentanglement of causally-related latent variables have been established in
stationary settings by leveraging temporal structure. However, in nonstationary
setting, existing work only partially addressed the problem by either utilizing
observed auxiliary variables (e.g., class labels and/or domain indexes) as side
information or assuming simplified latent causal dynamics. Both constrain the
method to a limited range of scenarios. In this study, we further explored the
Markov Assumption under time-delayed causally related process in nonstationary
setting and showed that under mild conditions, the independent latent
components can be recovered from their nonlinear mixture up to a permutation
and a component-wise transformation, without the observation of auxiliary
variables. We then introduce NCTRL, a principled estimation framework, to
reconstruct time-delayed latent causal variables and identify their relations
from measured sequential data only. Empirical evaluations demonstrated the
reliable identification of time-delayed latent causal influences, with our
methodology substantially outperforming existing baselines that fail to exploit
the nonstationarity adequately and then, consequently, cannot distinguish
distribution shifts.

在非平稳环境中，本研究通过探索具有时间延迟因果关系的过程下的马尔可夫假设，表明在温和条件下，可以从非线性混合中恢复独立的潜在成分，而无需观察辅助变量。我们还提出了 NCTRL，一种基于原则的估计框架，仅通过测量的序列数据重建时间延迟的潜在因果变量并确定它们之间的关系。经验评估表明，我们的方法可可靠地识别时间延迟的潜在因果影响，并在很大程度上胜过无法充分利用非平稳性并因此无法区分分布变化的现有基线方法。