  Recently in the field of unsupervised representation learning, strong
identifiability results for disentanglement of causally-related latent
variables have been established by exploiting certain side information, such as
class labels, in addition to independence. However, most existing work is
constrained by functional form assumptions such as independent sources or
further with linear transitions, and distribution assumptions such as
stationary, exponential family distribution. It is unknown whether the
underlying latent variables and their causal relations are identifiable if they
have arbitrary, nonparametric causal influences in between. In this work, we
establish the identifiability theories of nonparametric latent causal processes
from their nonlinear mixtures under fixed temporal causal influences and
analyze how distribution changes can further benefit the disentanglement. We
propose \textbf{\texttt{TDRL}}, a principled framework to recover time-delayed
latent causal variables and identify their relations from measured sequential
data under stationary environments and under different distribution shifts.
Specifically, the framework can factorize unknown distribution shifts into
transition distribution changes under fixed and time-varying latent causal
relations, and under observation changes in observation. Through experiments,
we show that time-delayed latent causal influences are reliably identified and
that our approach considerably outperforms existing baselines that do not
correctly exploit this modular representation of changes. Our code is available
at: \url{https://github.com/weirayao/tdrl}.
