Multi-Level Causal Embeddings

TL;DR

This paper introduces causal embeddings as a generalization of abstraction, enabling the mapping of multiple detailed causal models into coarser models, with applications in dataset merging and causal reasoning.

Contribution

It proposes a novel framework for multi-level causal embeddings, extending abstraction concepts and addressing the causal and statistical marginal problems.

Findings

Defined causal embeddings as a generalization of abstraction

Presented a multi-resolution marginal problem framework

Demonstrated practical use in merging datasets from different models

Abstract

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.