Abstraction between Structural Causal Models: A Review of Definitions and Properties

Fabio Massimo Zennaro

Keywords: causality, structural causal model, levels of abstraction, abstraction

TL;DR: A review of formal definitions of abstractions between SCMs, their formal properties at different levels (structural, distributional), and the types of abstractions they allow.

Abstract: Structural causal models (SCMs) are a widespread formalism to deal with causal systems. A recent direction of research has considered the problem of relating formally SCMs at different levels of abstraction, by defining maps between SCMs and imposing a requirement of interventional consistency. This paper offers a review of the solutions proposed so far, focusing on the formal properties of a map between SCMs, and highlighting the different levels (structural, distributional) at which these properties may be enforced. This allows us to distinguish families of abstractions that may or may not be permitted by choosing to guarantee certain properties instead of others. Such an understanding not only allows to distinguish among proposal for causal abstraction with more awareness, but it also allows to tailor the definition of abstraction with respect to the forms of abstraction relevant to specific applications.