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).

翻译：我们解决了从具有一系列不同未知体制的多元时间序列中进行结构学习的挑战。我们提出了一种新的基于优化的方法（CASTOR），该方法同时学习每个体制的有向无环图（DAG），并确定体制数量及其顺序排列。通过期望最大化（EM）算法优化评分函数，CASTOR交替学习体制索引（期望步骤）和推断每个体制中的因果关系（最大化步骤）。我们进一步证明了CASTOR框架内体制和DAG的可识别性。我们进行了广泛的实验，结果表明我们的方法在各种设置（线性和非线性因果关系）和数据集（合成和真实数据）中始终优于因果发现模型。