Causal Abstraction Inference under Lossy Representations

• URL: http://arxiv.org/abs/2509.21607v1
• Date: Thu, 25 Sep 2025 21:20:42 GMT
• Title: Causal Abstraction Inference under Lossy Representations
• Authors: Kevin Xia, Elias Bareinboim,
• Abstract summary: We introduce a new type of abstractions called projected abstractions that generalize existing definitions to accommodate lossy representations.<n>We show how to construct a projected abstraction from the low-level model and how it translates equivalent observational, interventional, and counterfactual causal queries from low to high-level.
• Score: 53.18851962820361
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The study of causal abstractions bridges two integral components of human intelligence: the ability to determine cause and effect, and the ability to interpret complex patterns into abstract concepts. Formally, causal abstraction frameworks define connections between complicated low-level causal models and simple high-level ones. One major limitation of most existing definitions is that they are not well-defined when considering lossy abstraction functions in which multiple low-level interventions can have different effects while mapping to the same high-level intervention (an assumption called the abstract invariance condition). In this paper, we introduce a new type of abstractions called projected abstractions that generalize existing definitions to accommodate lossy representations. We show how to construct a projected abstraction from the low-level model and how it translates equivalent observational, interventional, and counterfactual causal queries from low to high-level. Given that the true model is rarely available in practice we prove a new graphical criteria for identifying and estimating high-level causal queries from limited low-level data. Finally, we experimentally show the effectiveness of projected abstraction models in high-dimensional image settings.

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