Castor: Causal Temporal Regime Structure Learning

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. Multivariate Time Series (MTS) is a very common type of data in a wide variety of fields. Uncovering the causal relationships among MTS variables and understanding how they evolve over time is crucial in numerous fields, such as climate science and health care. Although randomized controlled trials are widely recognized as the definitive method for determining causal relationships (Hariton & Locascio, 2018; McCoy, 2017), they often present challenges in terms of cost, ethics, or feasibility. For example: learning gene regulatory networks via gene knockout experiments would be prohibitively expensive on a large scale. Consequently, a multitude of causal discovery approaches now focus on extracting causality from observational data sources (L owe et al., 2022; Bussmann et al., 2021; Pamfil et al., 2020; Moraffah et al., 2021; Runge, 2018; Wu et al., 2020).