Identifying Causal Effects Under Functional Dependencies
Yizuo Chen, Adnan Darwiche
TL;DR
The paper tackles identifying causal effects when some variables are known to be functionally determined by their parents, without requiring the explicit functional form. It introduces functional identifiability (F-identifiability) and develops functional elimination and functional projection to preserve relevant independencies, enabling the use of standard identifiability tools such as the ID algorithm under positivity constraints. Two complementary strategies are proposed to test and achieve F-identifiability: (a) reduce F-identifiability to classical identifiability by eliminating hidden functional variables and applying project-ID, and (b) treat certain hidden functionals as observed to leverage existing identifiability methods under weaker positivity; a complete fid result shows equivalence under specific conditions. The framework provides practical pathways to identify causal effects with fewer observed variables and clarifies when functional information can resolve unidentifiability, with proofs and technical details relegated to the Appendix.
Abstract
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.