# Cluster-Dags as Powerful Background Knowledge For Causal Discovery

arXiv: https://arxiv.org/abs/2512.10032 · HTML: https://mlsanity.com/paper/2512.10032/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 81 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 30 of 43)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Foundation Models for Causal Inference via Prior-Data Fitted Networks](https://mlsanity.com/paper/2506.10914/) (2025)
- [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)
- [Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation](https://mlsanity.com/paper/2311.11321/) (2023)
- [Identifiability of total effects from abstractions of time series causal graphs](https://mlsanity.com/paper/2310.14691/) (2023)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [Learning Structures of Bayesian Networks for Variable Groups](https://mlsanity.com/paper/1508.07753/) (2015)
- [Conditional Independence Testing in Hilbert Spaces with Applications to Functional Data Analysis](https://mlsanity.com/paper/2101.07108/) (2021)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [Vector causal inference between two groups of variables](https://mlsanity.com/paper/2209.14283/) (2022)
- [Characterization and Learning of Causal Graphs with Small Conditioning Sets](https://mlsanity.com/paper/2301.09028/) (2023)
- [Learning Causal Abstractions of Linear Structural Causal Models](https://mlsanity.com/paper/2406.00394/) (2024)
- [A Weaker Faithfulness Assumption based on Triple Interactions](https://mlsanity.com/paper/2010.14265/) (2020)
- [Typing assumptions improve identification in causal discovery](https://mlsanity.com/paper/2107.10703/) (2021)
- [Local Causal Discovery for Estimating Causal Effects](https://mlsanity.com/paper/2302.08070/) (2023)
- [Do we become wiser with time? On causal equivalence with tiered background knowledge](https://mlsanity.com/paper/2306.01638/) (2023)
- [Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confounding](https://mlsanity.com/paper/2407.07934/) (2024)
- [Evaluation of Induced Expert Knowledge in Causal Structure Learning by NOTEARS](https://mlsanity.com/paper/2301.01817/) (2023)
- [Aligning Graphical and Functional Causal Abstractions](https://mlsanity.com/paper/2412.17080/) (2024)
- [On the Representation of Pairwise Causal Background Knowledge and Its Applications in Causal Inference](https://mlsanity.com/paper/2207.05067/) (2022)
- [Optimizing Data-driven Causal Discovery Using Knowledge-guided Search](https://mlsanity.com/paper/2304.05493/) (2023)
- [Meaningful Causal Aggregation and Paradoxical Confounding](https://mlsanity.com/paper/2304.11625/) (2023)
- [Towards identifiability of micro total effects in summary causal graphs with latent confounding: extension of the front-door criterion](https://mlsanity.com/paper/2406.05805/) (2024)
- [Causal discovery on vector-valued variables and consistency-guided aggregation](https://mlsanity.com/paper/2505.10476/) (2025)

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

- [Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables](https://mlsanity.com/paper/2602.23611/) (2026)
- [GO-Based Clustering for Learning Cluster-Level Causal Gene Regulatory Networks](https://mlsanity.com/paper/2610.06042/) (2026)

## Abstract (arXiv)

Finding cause-effect relationships is of key importance in science. Causal discovery aims to recover a graph from data that succinctly describes these cause-effect relationships. However, current methods face several challenges, especially when dealing with high-dimensional data and complex dependencies. Incorporating prior knowledge about the system can aid causal discovery. In this work, we leverage Cluster-DAGs as a prior knowledge framework to warm-start causal discovery. We show that Cluster-DAGs offer greater flexibility than existing approaches based on tiered background knowledge and introduce two modified constraint-based algorithms, Cluster-PC and Cluster-FCI, for causal discovery in the fully and partially observed setting, respectively. Empirical evaluation on simulated data demonstrates that Cluster-PC and Cluster-FCI outperform their respective baselines without prior knowledge.