Causal discovery uncovers complex relationships between variables, enhancing predictions, decision-making, and insights into real-world systems, especially in nonlinear multivariate time series. However, most existing methods primarily focus on pairwise cause-effect relationships, overlooking interactions among groups of variables, i.e., subsystems and their collective causal influence. In this study, we introduce gCDMI, a novel multi-group causal discovery method that leverages group-level interventions on trained deep neural networks and employs model invariance testing to infer causal relationships. Our approach involves three key steps. First, we use deep learning to jointly model the structural relationships among groups of all time series. Second, we apply group-wise interventions to the trained model. Finally, we conduct model invariance testing to determine the presence of causal links among variable groups. We evaluate our method on simulated datasets, demonstrating its superior performance in identifying group-level causal relationships compared to existing methods. Additionally, we validate our approach on real-world datasets, including brain networks and climate ecosystems. Our results highlight that applying group-level interventions to deep learning models, combined with invariance testing, can effectively reveal complex causal structures, offering valuable insights for domains such as neuroscience and climate science.

翻译：因果发现揭示了变量间的复杂关系，可提升对现实世界系统的预测能力、决策水平及机制理解，尤其在非线性多元时间序列分析中具有重要意义。然而，现有方法大多聚焦于变量间的成对因果关系，忽视了变量组（即子系统）间的交互作用及其集体因果效应。本研究提出一种新颖的多群体因果发现方法gCDMI，该方法通过对训练后的深度神经网络实施群体层面的干预，并利用模型不变性检验来推断因果关系。我们的方法包含三个关键步骤：首先，采用深度学习对全部时间序列的群体结构关系进行联合建模；其次，对训练后的模型实施分组干预；最后，通过模型不变性检验判定变量组间是否存在因果关联。我们在模拟数据集上评估了该方法，结果表明其在识别群体层面因果关系方面优于现有方法。此外，我们在脑网络和气候生态系统等真实数据集上验证了该方法的有效性。研究结果证明，对深度学习模型实施群体干预并结合不变性检验，能够有效揭示复杂的因果结构，为神经科学和气候科学等领域提供重要洞见。