Understanding causal relationships in multivariate time series is crucial in many scenarios, such as those dealing with financial or neurological data. Many such time series exhibit multiple regimes, i.e., consecutive temporal segments with a priori unknown boundaries, with each regime having its own causal structure. Inferring causal dependencies and regime shifts is critical for analyzing the underlying processes. However, causal structure learning in this setting is challenging due to (1) non stationarity, i.e., each regime can have its own causal graph and mixing function, and (2) complex noise distributions, which may be non Gaussian or heteroscedastic. Existing causal discovery approaches cannot address these challenges, since generally assume stationarity or Gaussian noise with constant variance. Hence, we introduce FANTOM, a unified framework for causal discovery that handles non stationary processes along with non Gaussian and heteroscedastic noises. FANTOM simultaneously infers the number of regimes and their corresponding indices and learns each regime's Directed Acyclic Graph. It uses a Bayesian Expectation Maximization algorithm that maximizes the evidence lower bound of the data log likelihood. On the theoretical side, we prove, under mild assumptions, that temporal heteroscedastic causal models, introduced in FANTOM's formulation, are identifiable in both stationary and non stationary settings. In addition, extensive experiments on synthetic and real data show that FANTOM outperforms existing methods.

翻译：理解多元时间序列中的因果关系在许多场景中至关重要，例如处理金融或神经科学数据的场景。许多此类时间序列表现出多重机制，即具有先验未知边界的连续时间片段，每个机制都有其自身的因果结构。推断因果依赖关系和机制转换对于分析底层过程至关重要。然而，在这种设置下进行因果结构学习具有挑战性，原因在于：(1) 非平稳性，即每个机制可能具有各自的因果图和混合函数；(2) 复杂的噪声分布，这些噪声可能非高斯或具有异方差性。现有的因果发现方法无法应对这些挑战，因为它们通常假设平稳性或具有恒定方差的高斯噪声。因此，我们提出了FANTOM，一个统一的因果发现框架，能够处理非平稳过程以及非高斯和异方差噪声。FANTOM同时推断机制数量及其对应索引，并学习每个机制的有向无环图。它采用贝叶斯期望最大化算法，最大化数据对数似然的证据下界。在理论方面，我们证明在温和假设下，FANTOM公式中引入的时序异方差因果模型在平稳和非平稳设置下均可识别。此外，在合成数据和真实数据上的大量实验表明，FANTOM优于现有方法。