arXiv Machine Learning October 5, 2026 By Jani Nyk\"anen, Otto Tabell, Santtu Tikka, Juha Karvanen

Invariance of Clustering Operations in Causal Effect Identification

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The paper studies how clustering variables in causal graphs can simplify inference but may also distort causal relations. It defines an "identification invariant" clustering operation—one that preserves both identifiability and nonidentifiability of causal effects—and presents a broad class of such operations based on conditions involving the c‑components of the original graph. The authors illustrate the practical application of these results in real‑world settings.

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