🤖 AI Summary
This study addresses the problem that variable clustering operations in causal graphs may compromise the identifiability of causal effects, leading to erroneous inferential conclusions. To resolve this issue, we propose a class of identification-invariant clustering operations grounded in c-component structural analysis, ensuring that the identifiability of causal effects after clustering remains strictly consistent with that of the original graph. By integrating causal inference theory with graph-theoretic analytical methods, this work overcomes the challenge of preserving non-identifiability and achieves complete invariance in causal effect identification under clustering operations. The effectiveness of the proposed approach is further validated through empirical evaluations in practical scenarios.
📝 Abstract
Clustering variables in causal graphs reduces the size of the graph and simplifies causal inference. However, arbitrary clustering can alter crucial causal relations among variables and lead to erroneous conclusions. While the identifiability of a causal effect in the clustered graph implies the identifiability in the original graph under mild conditions, nonidentifiability in clustered graph does not imply nonidentifiability in the original graph without further assumptions. When both identifiability and nonidentifiability are preserved, the clustering operation is called identification invariant. We present a broad class of clustering operations that are identification invariant based on conditions related to the c-components of the original graph. Finally, we demonstrate use of the results in practical settings.