  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.
