Identifying Causal Effects Under Functional Dependencies
This work addresses a theoretical bottleneck in causal inference for researchers, offering incremental improvements by leveraging functional dependencies without requiring specific function knowledge.
The paper tackles the problem of identifying causal effects when some variables are functionally determined by their parents, showing that this knowledge can make previously unidentifiable effects identifiable and reduce the number of variables needed in observational data.
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.