# Quantifying Consistency and Information Loss for Causal Abstraction Learning

arXiv: https://arxiv.org/abs/2305.04357 · HTML: https://mlsanity.com/paper/2305.04357/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 7 May 2023.

## Builds on (most cited first, 13 of 13)

- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics](https://mlsanity.com/paper/1908.07021/) (2019)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [When the map is better than the territory](https://mlsanity.com/paper/1612.09592/) (2016)
- [On the Equivalence of Causal Models: A Category-Theoretic Approach](https://mlsanity.com/paper/2201.06981/) (2022)
- [Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity](https://mlsanity.com/paper/1812.09414/) (2018)
- [Refinement and Coarsening of Bayesian Networks](https://mlsanity.com/paper/1304.1138/) (2013)

## Built on by (most cited first, 7 of 7)

- [Interventionally Consistent Surrogates for Agent-based Simulators](https://mlsanity.com/paper/2312.11158/) (2023)
- [Causally Abstracted Multi-armed Bandits](https://mlsanity.com/paper/2404.17493/) (2024)
- [Identifiability in Causal Abstractions: A Hierarchy of Criteria](https://mlsanity.com/paper/2507.06213/) (2025)
- [Using causal abstractions to accelerate decision-making in complex bandit problems](https://mlsanity.com/paper/2509.04296/) (2025)
- [Partial Effective Information Decomposition for Synergistic Causality](https://mlsanity.com/paper/2605.03267/) (2026)
- [Validating Causal Abstraction Metrics on Simulated Complex Systems](https://mlsanity.com/paper/2607.00267/) (2026)
- [Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria](https://mlsanity.com/paper/2610.13520/) (2026)

## Abstract (arXiv)

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.