The task of uncovering causal relationships among multivariate time series
data stands as an essential and challenging objective that cuts across a broad
array of disciplines ranging from climate science to healthcare. Such data
entails linear or non-linear relationships, and usually follow multiple a
priori unknown regimes. Existing causal discovery methods can infer summary
causal graphs from heterogeneous data with known regimes, but they fall short
in comprehensively learning both regimes and the corresponding causal graph. In
this paper, we introduce CASTOR, a novel framework designed to learn causal
relationships in heterogeneous time series data composed of various regimes,
each governed by a distinct causal graph. Through the maximization of a score
function via the EM algorithm, CASTOR infers the number of regimes and learns
linear or non-linear causal relationships in each regime. We demonstrate the
robust convergence properties of CASTOR, specifically highlighting its
proficiency in accurately identifying unique regimes. Empirical evidence,
garnered from exhaustive synthetic experiments and two real-world benchmarks,
confirm CASTOR's superior performance in causal discovery compared to baseline
methods. By learning a full temporal causal graph for each regime, CASTOR
establishes itself as a distinctly interpretable method for causal discovery in
heterogeneous time series.

通过最大化得分函数，使用 EM 算法学习各种制度中的线性或非线性因果关系，我们引入了 CASTOR，这是一个专门设计用于学习异构时间序列数据中的因果关系的新框架。