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

TL;DR

This paper reviews formal definitions and properties of abstraction between structural causal models (SCMs), analyzing how different levels of properties influence the feasibility and application of causal abstractions.

Contribution

It systematically reviews existing solutions for SCM abstraction, focusing on formal properties and layers, enabling tailored and more informed causal abstraction definitions.

Findings

Identifies different layers (structural, distributional) for enforcing properties.

Distinguishes families of abstractions based on property guarantees.

Provides insights for application-specific causal abstraction design.

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 layers (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.