Causal Abstraction Inference under Lossy Representations
This work addresses a limitation in causal abstraction theory for researchers in causal inference and AI, offering a more flexible framework that is incremental but extends applicability to real-world scenarios with lossy data.
The paper tackles the problem of causal abstraction inference under lossy representations, where existing frameworks fail due to the abstract invariance condition, by introducing projected abstractions that generalize definitions to handle lossy cases and proving graphical criteria for estimation from limited data, with experimental validation in high-dimensional image settings.
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.