Quantifying Consistency and Information Loss for Causal Abstraction Learning
This work addresses a foundational challenge in causal modeling for researchers and practitioners, offering tools to optimize abstraction choices, though it is incremental in building on existing causal abstraction frameworks.
The paper tackles the problem of evaluating the trade-off between consistency and information loss when switching between different levels of abstraction in structural causal models, introducing a family of interventional measures and algorithms for learning causal abstractions, with empirical results showing how different measures lead to varied abstractions.
Structural causal models provide a formalism to express causal relations between variables of interest. Models and variables can represent a system at different levels of abstraction, whereby relations may be coarsened and refined according to the need of a modeller. However, switching between different levels of abstraction requires evaluating a trade-off between the consistency and the information loss among different models. In this paper we introduce a family of interventional measures that an agent may use to evaluate such a trade-off. We consider four measures suited for different tasks, analyze their properties, and propose algorithms to evaluate and learn causal abstractions. Finally, we illustrate the flexibility of our setup by empirically showing how different measures and algorithmic choices may lead to different abstractions.