Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria

Clément Yvernes; Marianne Clausel; Emilie Devijver; Eric Gaussier

cs.AIOct 9, 2026

Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria

Authors: Clément Yvernes, Marianne Clausel, Emilie Devijver, Eric Gaussier

Organizations: Univ Grenoble Alpes, CNRS, Grenoble INP, LIG · Université de Lorraine, CNRS, CRAN, 54000 Nancy

Abstract

Identifying causal effects from observational data typically requires a fully specified causal graph, an assumption that is often unrealistic in complex or high-dimensional settings. Causal abstractions address this limitation by retaining only partial causal information, thereby defining equivalence classes of compatible causal graphs. In this paper, we study causal effect identifiability directly at the level of these graph collections, rather than at the level of individual causal diagrams. We formalize several notions of identifiability in this setting and organize them into a hierarchy that clarifies their relationships and differences. In particular, we establish that a causal effect may be identified over a collection of graphs without admitting a single causal derivation that holds uniformly across all compatible graphs. These results help reveal gaps and clarify ambiguities in the existing literature.

Figures & tables

Panel of Figure 1 — Figure 1: Hierarchy between the notions of identifiability. An arrow indicates that the implication holds in every case. A red cross on an arrow indicates that the implication fails in at least one case.

Panel of Figure 2 — Figure 2: Derivation graph of the DAG from Example 2 . Blue nodes denote interventional queries, while orange nodes denote do-free queries. Edges of the derivation graph represent valid applications of the do-calculus rules in the DAG: gray solid lines for Rule $\mathcal{R}1$ , orange dashed lines for Rule $\mathcal{R}2$ , and blue dotted lines for Rule $\mathcal{R}3$ . Only vertices that are non-isolated are displayed.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 3 — Figure 3: The Napkin Graph ( Pearl and Mackenzie, 2018 ; Guo et al., 2025 )

Panel of Figure 4 — Figure 4: Intersection of the derivations graphs of ${\mathcal{G}}_{1}$ and ${\mathcal{G}}_{2}$ . Blue nodes denote interventional queries, while orange nodes denote do-free queries. Edges represent applications of the do-calculus rules: gray solid lines for Rule $\mathcal{R}1$ , orange dashed lines for Rule $\mathcal{R}2$ , and blue dotted lines for Rule $\mathcal{R}3$ . Only non-isolated queries are displayed.

Panel of Figure 5 — Figure 5: Derivation graph of ${\mathcal{G}}_{3}$ . Blue nodes denote interventional queries, while orange nodes denote do-free queries. Edges represent applications of the do-calculus rules: gray solid lines for Rule $\mathcal{R}1$ , orange dashed lines for Rule $\mathcal{R}2$ , and blue dotted lines for Rule $\mathcal{R}3$ . Only non isolated queries are displayed.

Causal Identifiability

Causal identifiability asks when data and stated assumptions uniquely determine causal structures, effects, or counterfactuals.

See all 128 papers

Invariance of Clustering Operations in Causal Effect Identification
Oct 2, 2026Jani Nykänen, Otto Tabell, Santtu Tikka +1Causal Identifiability Causal Effect Estimation
Department of Mathematics and Statistics FI-40014 University of Jyvaskyla, Finland
Efficient Symbolic Computations for Identifying Causal Effects
Apr 22, 2026Benjamin Hollering, Pratik Misra, Nils SturmaStructural Causal Models Symbolic Reasoning
Max Planck Institute for Mathematics in the Sciences, Germany · Binghamton University, USA · École Polytechnique Fédérale de Lausanne, Switzerland
Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems
Mar 9, 2026Gijs van Seeventer, Saber SalehkaleybarStochastic Differential Equations Structural Causal Models
1LIACS, Leiden University, Netherlands

Oct 2, 2026J/K move · Enter open · S save

Invariance of Clustering Operations in Causal Effect Identification

Jani Nykänen, Otto Tabell, Santtu Tikka, Juha Karvanen

Department of Mathematics and Statistics FI-40014 University of Jyvaskyla, Finland

Causal Identifiability Causal Effect Estimation Structural Causal Models

Open paper AskPDF arXiv

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.

Abstract

Causal Identifiability

Explore similar work

Invariance of Clustering Operations in Causal Effect Identification

Efficient Symbolic Computations for Identifying Causal Effects

Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems