Multi-Level Causal Embeddings
This work addresses a foundational issue in causal inference for researchers and practitioners dealing with heterogeneous data, though it appears incremental as it builds on existing abstraction frameworks.
The paper tackles the problem of merging datasets from models with different representations by generalizing causal abstractions to multi-level causal embeddings, enabling multiple detailed models to map into a coarser causal model while preserving cause-effect relations.
Abstractions of causal models allow for the coarsening of models such that relations of cause and effect are preserved. Whereas abstractions focus on the relation between two models, in this paper we study a framework for causal embeddings which enable multiple detailed models to be mapped into sub-systems of a coarser causal model. We define causal embeddings as a generalization of abstraction, and present a generalized notion of consistency. By defining a multi-resolution marginal problem, we showcase the relevance of causal embeddings for both the statistical marginal problem and the causal marginal problem; furthermore, we illustrate its practical use in merging datasets coming from models with different representations.