Causal systems often exhibit variations of the underlying causal mechanisms between the variables of the system. Often, these changes are driven by different environments or internal states in which the system operates, and we refer to context variables as those variables that indicate this change in causal mechanisms. An example are the causal relations in soil moisture-temperature interactions and their dependence on soil moisture regimes: Dry soil triggers a dependence of soil moisture on latent heat, while environments with wet soil do not feature such a feedback, making it a context-specific property. Crucially, a regime or context variable such as soil moisture need not be exogenous and can be influenced by the dynamical system variables - precipitation can make a dry soil wet - leading to joint systems with endogenous context variables. In this work we investigate the assumptions for constraint-based causal discovery of context-specific information in systems with endogenous context variables. We show that naive approaches such as learning different regime graphs on masked data, or pooling all data, can lead to uninformative results. We propose an adaptive constraint-based discovery algorithm and give a detailed discussion on the connection to structural causal models, including sufficiency assumptions, which allow to prove the soundness of our algorithm and to interpret the results causally. Numerical experiments demonstrate the performance of the proposed method over alternative baselines, but they also unveil current limitations of our method.

翻译：因果系统通常表现出系统变量间潜在因果机制的变化。这些变化往往由系统运行的不同环境或内部状态所驱动，我们将指示这种因果机制变化的变量称为情境变量。例如土壤湿度-温度相互作用中的因果关系及其对土壤湿度状况的依赖性：干燥土壤会触发土壤湿度对潜热的依赖，而湿润土壤环境则不存在这种反馈，这使其成为情境特异性属性。关键在于，诸如土壤湿度这样的状态或情境变量未必是外生的，它可能受到动力系统变量的影响——降水可使干燥土壤变得湿润——从而形成具有内生情境变量的联合系统。本研究探讨了在具有内生情境变量的系统中，基于约束的因果发现方法获取情境特异性信息所需的前提假设。我们证明，诸如在掩蔽数据上学习不同状态图或直接合并所有数据等简单方法可能导致无意义的结果。我们提出了一种自适应约束发现算法，并详细讨论了其与结构因果模型的关联，包括充分性假设——这些假设使我们能够证明算法的可靠性并对结果进行因果解释。数值实验表明所提方法相较于替代基线具有更优性能，同时也揭示了当前方法的局限性。