Towards Computing an Optimal Abstraction for Structural Causal Models

Fabio Massimo Zennaro, Paolo Turrini, Theo Damoulas

Keywords: structural causal models, SCM, abstraction, levels of abstraction, learning

TL;DR: Defining an optimization problem for learning abstractions between causal models and proposing a measure of information loss for its objective function.

Abstract: Working with causal model 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.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2208.00894/code)