# Identifiability in Causal Abstractions: A Hierarchy of Criteria

arXiv: https://arxiv.org/abs/2507.06213 · HTML: https://mlsanity.com/paper/2507.06213/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 8 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Foundations of Causal Discovery on Groups of Variables](https://mlsanity.com/paper/2306.07047/) (2023)
- [Identifiability of total effects from abstractions of time series causal graphs](https://mlsanity.com/paper/2310.14691/) (2023)
- [Learning Structures of Bayesian Networks for Variable Groups](https://mlsanity.com/paper/1508.07753/) (2015)
- [Quantifying Consistency and Information Loss for Causal Abstraction Learning](https://mlsanity.com/paper/2305.04357/) (2023)
- [Causally Abstracted Multi-armed Bandits](https://mlsanity.com/paper/2404.17493/) (2024)
- [Towards Computing an Optimal Abstraction for Structural Causal Models](https://mlsanity.com/paper/2208.00894/) (2022)
- [Complete Characterization for Adjustment in Summary Causal Graphs of Time Series](https://mlsanity.com/paper/2506.14534/) (2025)

## Built on by (most cited first, 2 of 2)

- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria](https://mlsanity.com/paper/2610.13520/) (2026)

## Abstract (arXiv)

Identifying the effect of a treatment from observational data typically requires assuming a fully specified causal diagram. However, such diagrams are rarely known in practice, especially in complex or high-dimensional settings. To overcome this limitation, recent works have explored the use of causal abstractions-simplified representations that retain partial causal information. In this paper, we consider causal abstractions formalized as collections of causal diagrams, and focus on the identifiability of causal queries within such collections. We introduce and formalize several identifiability criteria under this setting. Our main contribution is to organize these criteria into a structured hierarchy, highlighting their relationships. This hierarchical view enables a clearer understanding of what can be identified under varying levels of causal knowledge. We illustrate our framework through examples from the literature and provide tools to reason about identifiability when full causal knowledge is unavailable.