We study the identification of causal effects, motivated by two improvements to identifiability which can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Second, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure which removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects.

翻译：我们研究因果效应的识别问题，其动机源于两种可识别性的改进：若已知因果图中某些变量由父节点函数决定（无需知晓具体函数形式），则可实现这些改进。首先，当某些变量为函数型时，原本无法识别的因果效应可能变得可识别。其次，某些函数型变量可在不影响因果效应可识别性的前提下从观测中排除，这能显著减少观测数据所需的变量数量。我们的结论主要基于一种消去程序，该程序从因果图中移除函数型变量，同时保留结果因果图的关键性质（包括因果效应的可识别性）。