Discovering causal relationships from time series data is significant in fields such as finance, climate science, and neuroscience. However, contemporary techniques rely on the simplifying assumption that data originates from the same causal model, while in practice, data is heterogeneous and can stem from different causal models. In this work, we relax this assumption and perform causal discovery from time series data originating from a mixture of causal models. We propose a general variational inference-based framework called MCD to infer the underlying causal models as well as the mixing probability of each sample. Our approach employs an end-to-end training process that maximizes an evidence-lower bound for the data likelihood. We present two variants: MCD-Linear for linear relationships and independent noise, and MCD-Nonlinear for nonlinear causal relationships and history-dependent noise. We demonstrate that our method surpasses state-of-the-art benchmarks in causal discovery tasks through extensive experimentation on synthetic and real-world datasets, particularly when the data emanates from diverse underlying causal graphs. Theoretically, we prove the identifiability of such a model under some mild assumptions.

翻译：从时间序列数据中发现因果关系在金融、气候科学和神经科学等领域具有重要意义。然而，现有技术依赖于数据源自同一因果模型这一简化假设，而在实践中，数据具有异质性，可能源自不同的因果模型。在本工作中，我们放宽了这一假设，对源自混合因果模型的时间序列数据进行因果发现。我们提出了一个通用的基于变分推理的框架，称为MCD，用于推断潜在的因果模型以及每个样本的混合概率。我们的方法采用端到端的训练过程，最大化数据似然的证据下界。我们提出了两个变体：用于线性关系和独立噪声的MCD-Linear，以及用于非线性因果关系和历史依赖噪声的MCD-Nonlinear。通过在合成和真实世界数据集上的大量实验，我们证明了我们的方法在因果发现任务中超越了最先进的基准，尤其是在数据源自不同底层因果图的情况下。理论上，我们在一些温和假设下证明了此类模型的可识别性。