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的简化假设，而实际中数据具有异质性，可能来自不同的因果模型。本研究放宽了这一假设，针对混合因果模型生成的时间序列数据开展因果关系发现。我们提出一个基于变分推断的通用框架MCD，用于推断潜在因果模型及每个样本的混合概率。该方法采用端到端训练过程，最大化数据似然的证据下界。我们提供了两种变体：针对线性关系与独立噪声的MCD-Linear，以及针对非线性因果关系与历史依赖噪声的MCD-Nonlinear。通过在合成数据集和真实世界数据集上的广泛实验，我们证明了该方法在因果发现任务中超越现有最优基准，尤其当数据源自多种不同的底层因果图时。理论上，我们证明了在温和假设下该模型的可识别性。