Abstracting Causal Models
This work addresses foundational issues in causal modeling for researchers in AI and statistics, but it is incremental as it builds on prior definitions.
The paper tackles the problem of defining abstraction for causal models by introducing a sequence of increasingly restrictive definitions, culminating in strong abstraction, and shows that variable combination procedures and prior examples are instances of this notion.
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.