Equivalent Causal Models

TL;DR

This paper systematically explores and defines the concept of equivalent causal models, focusing on models with different variables but sharing essential causal information through their structural and functional relations.

Contribution

It introduces a formal framework for understanding equivalence of causal models with different variables, emphasizing preservation of causal relations.

Findings

Defined relations of causal ancestry and sufficiency

Established criteria for model equivalence based on these relations

Provided a foundational framework for comparing diverse causal models

Abstract

The aim of this paper is to offer the first systematic exploration and definition of equivalent causal models in the context where both models are not made up of the same variables. The idea is that two models are equivalent when they agree on all "essential" causal information that can be expressed using their common variables. I do so by focussing on the two main features of causal models, namely their structural relations and their functional relations. In particular, I define several relations of causal ancestry and several relations of causal sufficiency, and require that the most general of these relations are preserved across equivalent models.