Identifiability in Causal Abstractions: A Hierarchy of Criteria
This work addresses the challenge of causal inference in complex or high-dimensional settings where full causal diagrams are rarely known, offering a structured framework for researchers and practitioners, though it is incremental as it builds on existing causal abstraction concepts.
The paper tackles the problem of identifying causal effects from observational data without requiring a fully specified causal diagram by formalizing identifiability criteria within causal abstractions, and it organizes these criteria into a hierarchy to clarify what can be identified under varying levels of causal knowledge.
Identifying the effect of a treatment from observational data typically requires assuming a fully specified causal diagram. However, such diagrams are rarely known in practice, especially in complex or high-dimensional settings. To overcome this limitation, recent works have explored the use of causal abstractions-simplified representations that retain partial causal information. In this paper, we consider causal abstractions formalized as collections of causal diagrams, and focus on the identifiability of causal queries within such collections. We introduce and formalize several identifiability criteria under this setting. Our main contribution is to organize these criteria into a structured hierarchy, highlighting their relationships. This hierarchical view enables a clearer understanding of what can be identified under varying levels of causal knowledge. We illustrate our framework through examples from the literature and provide tools to reason about identifiability when full causal knowledge is unavailable.