Towards Computing an Optimal Abstraction for Structural Causal Models

TL;DR

This paper addresses the challenge of learning optimal abstractions for structural causal models by extending existing measures with an information loss term, aiming to improve the quality of causal abstractions.

Contribution

It formalizes the learning problem of causal model abstractions and introduces an extension to the objective function that accounts for information loss.

Findings

Extended the abstraction learning objective with an information loss term

Proposed a concrete measure of information loss

Illustrated the impact of the new measure on learning abstractions

Abstract

Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we focus on the problem of learning abstractions. We start by defining the learning problem formally in terms of the optimization of a standard measure of consistency. We then point out the limitation of this approach, and we suggest extending the objective function with a term accounting for information loss. We suggest a concrete measure of information loss, and we illustrate its contribution to learning new abstractions.