# Coarsening Causal DAG Models

arXiv: https://arxiv.org/abs/2601.10531 · HTML: https://mlsanity.com/paper/2601.10531/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 66 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Builds on (most cited first, 30 of 34)

- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [Multi-Level Cause-Effect Systems](https://mlsanity.com/paper/1512.07942/) (2015)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [Foundations of Causal Discovery on Groups of Variables](https://mlsanity.com/paper/2306.07047/) (2023)
- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Causal Structure Discovery between Clusters of Nodes Induced by Latent Factors](https://mlsanity.com/paper/2207.01237/) (2022)
- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [Measurement Dependence Inducing Latent Causal Models](https://mlsanity.com/paper/1910.08778/) (2019)
- [Learning big Gaussian Bayesian networks: partition, estimation, and fusion](https://mlsanity.com/paper/1904.10900/) (2019)
- [On the Equivalence of Causal Models: A Category-Theoretic Approach](https://mlsanity.com/paper/2201.06981/) (2022)
- [Causal Optimal Transport of Abstractions](https://mlsanity.com/paper/2312.08107/) (2023)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [Vector causal inference between two groups of variables](https://mlsanity.com/paper/2209.14283/) (2022)
- [Learning Causal Abstractions of Linear Structural Causal Models](https://mlsanity.com/paper/2406.00394/) (2024)
- [A Distance Covariance-based Kernel for Nonlinear Causal Clustering in Heterogeneous Populations](https://mlsanity.com/paper/2106.03480/) (2021)
- [Do we become wiser with time? On causal equivalence with tiered background knowledge](https://mlsanity.com/paper/2306.01638/) (2023)
- [Causal Abstraction Learning based on the Semantic Embedding Principle](https://mlsanity.com/paper/2502.00407/) (2025)
- [Aligning Graphical and Functional Causal Abstractions](https://mlsanity.com/paper/2412.17080/) (2024)
- [Nonlinear Causal Discovery for Grouped Data](https://mlsanity.com/paper/2506.05120/) (2025)
- [Equivalent Causal Models](https://mlsanity.com/paper/2012.05603/) (2020)
- [A Transformational Characterization of Unconditionally Equivalent Bayesian Networks](https://mlsanity.com/paper/2203.00521/) (2022)
- [Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networks](https://mlsanity.com/paper/2210.00822/) (2022)

## Built on by (most cited first, 4 of 4)

- [Coarsening Linear Non-Gaussian Causal Models with Cycles](https://mlsanity.com/paper/2605.10163/) (2026)
- [Invariance of Clustering Operations in Causal Effect Identification](https://mlsanity.com/paper/2610.03101/) (2026)
- [GO-Based Clustering for Learning Cluster-Level Causal Gene Regulatory Networks](https://mlsanity.com/paper/2610.06042/) (2026)
- [Score-Based Learning of Cluster DAGs from Interventions](https://mlsanity.com/paper/2610.11947/) (2026)

## Abstract (arXiv)

Directed acyclic graphical (DAG) models are a powerful tool for representing causal relationships among jointly distributed random variables, especially concerning data from across different experimental settings. However, it is not always practical or desirable to estimate a causal model at the granularity of given features in a particular dataset. There is a growing body of research on causal abstraction to address such problems. We contribute to this line of research by (i) providing novel graphical identifiability results for practically-relevant interventional settings, (ii) proposing an efficient, provably consistent algorithm for directly learning abstract causal graphs from interventional data with unknown intervention targets, and (iii) uncovering theoretical insights about the lattice structure of the underlying search space, with connections to the field of causal discovery more generally. As proof of concept, we apply our algorithm on synthetic and real datasets with known ground truths, including measurements from a controlled physical system with interacting light intensity and polarization.