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：本文研究因果效应的识别问题，其动机源于在已知因果图中某些变量由其父节点函数决定（无需知晓具体函数形式）时可能实现的两个可识别性改进。首先，当特定变量具有函数依赖性时，原本不可识别的因果效应可能变得可识别。其次，某些函数变量可以从观测变量中排除而不影响因果效应的可识别性，这有望显著减少观测数据所需的变量数量。我们的研究成果主要基于一种消元方法，该方法能在保持因果效应可识别性等关键性质的前提下，从因果图中移除函数变量。