  We address the challenge of structure learning from multivariate time series
that are characterized by a sequence of different, unknown regimes. We
introduce a new optimization-based method (CASTOR), that concurrently learns
the Directed Acyclic Graph (DAG) for each regime and determine the number of
regimes along with their sequential arrangement. Through the optimization of a
score function via an expectation maximization (EM) algorithm, CASTOR
alternates between learning the regime indices (Expectation step) and inferring
causal relationships in each regime (Maximization step). We further prove the
identifiability of regimes and DAGs within the CASTOR framework. We conduct
extensive experiments and show that our method consistently outperforms causal
discovery models across various settings (linear and nonlinear causal
relationships) and datasets (synthetic and real data).
