Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for causal discovery when objects of interest are (multivariate) groups of random variables rather than individual (univariate) random variables, as is the case in a variety of problems in scientific domains such as climate science or neuroscience. If the group-level causal models are derived from partitioning a micro-level model into groups, we explore the relationship between micro and group-level causal discovery assumptions. We investigate the conditions under which assumptions like Causal Faithfulness hold or fail to hold. Our analysis encompasses graphical causal models that contain cycles and bidirected edges. We also discuss grouped time series causal graphs and variants thereof as special cases of our general theoretical framework. Thereby, we aim to provide researchers with a solid theoretical foundation for the development and application of causal discovery methods for variable groups.

翻译：从观测数据中发现因果关系是一项具有挑战性的任务，它依赖于将统计量与图模型或代数因果模型相联系的假设。本研究聚焦于当研究对象为（多元）随机变量组而非单个（单变量）随机变量时广泛采用的因果发现假设——例如气候科学或神经科学等科学领域中的多种问题。若分组因果模型源自将微观层面的模型划分为若干组，我们将探讨微观与分组层面因果发现假设之间的关系。我们研究了因果忠实性等假设成立或不成立的条件。我们的分析涵盖了包含循环边和双向边的图因果模型。此外，我们还讨论了分组时间序列因果图及其变体，将其作为我们通用理论框架的特例。由此，我们旨在为研究者开发和应用面向变量组的因果发现方法提供坚实的理论基础。