# Abstracting Causal Models

## TL;DR

This paper explores a hierarchy of abstraction concepts in causal models, from exact transformations to strong abstractions, providing a unified framework and showing how micro-variable combinations fit into this hierarchy.

## Contribution

It introduces a unified hierarchy of causal model abstractions and demonstrates that micro-variable aggregation is an instance of strong abstraction.

## Key findings

- Procedures for micro-variable aggregation are instances of strong abstraction.
- The hierarchy clarifies relationships among different causal abstraction notions.
- All examples by Rubenstein et al. fit into the strong abstraction framework.

## Abstract

We consider a sequence of successively more restrictive definitions of abstraction for causal models, starting with a notion introduced by Rubenstein et al. (2017) called exact transformation that applies to probabilistic causal models, moving to a notion of uniform transformation that applies to deterministic causal models and does not allow differences to be hidden by the "right" choice of distribution, and then to abstraction, where the interventions of interest are determined by the map from low-level states to high-level states, and strong abstraction, which takes more seriously all potential interventions in a model, not just the allowed interventions. We show that procedures for combining micro-variables into macro-variables are instances of our notion of strong abstraction, as are all the examples considered by Rubenstein et al.