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联系起来的假设。本文聚焦于研究对象为（多变量）随机变量组而非单个（单变量）随机变量时广泛使用的因果发现假设，这一情形常见于气候科学或神经科学等科学领域的多种问题中。当组级因果模型由微观级别模型分组导出时，我们探讨了微观与组级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。分析涵盖了包含环和双向边的图因果模型。我们还讨论了分组时间序列因果图及其变体，作为一般理论框架的特例。通过本研究，我们旨在为研究者开发和应用变量组因果发现方法提供坚实的理论基础。