# Foundations of Causal Discovery on Groups of Variables

arXiv: https://arxiv.org/abs/2306.07047 · HTML: https://mlsanity.com/paper/2306.07047/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2023.

## Built on by (most cited first, 22 of 22)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Learning Causal Abstractions of Linear Structural Causal Models](https://mlsanity.com/paper/2406.00394/) (2024)
- [Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confounding](https://mlsanity.com/paper/2407.07934/) (2024)
- [Aligning Graphical and Functional Causal Abstractions](https://mlsanity.com/paper/2412.17080/) (2024)
- [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)
- [Nonlinear Causal Discovery for Grouped Data](https://mlsanity.com/paper/2506.05120/) (2025)
- [Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering](https://mlsanity.com/paper/2511.01396/) (2025)
- [Identifying Macro Causal Effects in a C-DMG over ADMGs](https://mlsanity.com/paper/2504.01551/) (2025)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Structural Causal Bottleneck Models](https://mlsanity.com/paper/2603.08682/) (2026)
- [Identifying Macro Causal Effects in C-DMGs over DMGs](https://mlsanity.com/paper/2506.19650/) (2025)
- [Systems with Switching Causal Relations: A Meta-Causal Perspective](https://mlsanity.com/paper/2410.13054/) (2024)
- [Causal reasoning in difference graphs](https://mlsanity.com/paper/2411.01292/) (2024)
- [Identifiability in Causal Abstractions: A Hierarchy of Criteria](https://mlsanity.com/paper/2507.06213/) (2025)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Average Controlled and Average Natural Micro Direct Effects in Summary Causal Graphs](https://mlsanity.com/paper/2410.23975/) (2024)
- [Joint Causal Structure and Cluster Discovery Using Variational Inference](https://mlsanity.com/paper/2608.22212/) (2026)
- [Orientability of Causal Relations in Time Series using Summary Causal Graphs and Faithful Distributions](https://mlsanity.com/paper/2508.21742/) (2025)
- [Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables](https://mlsanity.com/paper/2602.23611/) (2026)
- [From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables](https://mlsanity.com/paper/2604.22416/) (2026)
- [Invariance of Clustering Operations in Causal Effect Identification](https://mlsanity.com/paper/2610.03101/) (2026)
- [Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria](https://mlsanity.com/paper/2610.13520/) (2026)

## Abstract (arXiv)

Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for causal discovery when objects of interest are (multivariate) groups of random variables rather than individual (univariate) random variables, as is the case in a variety of problems in scientific domains such as climate science or neuroscience. If the group-level causal models are derived from partitioning a micro-level model into groups, we explore the relationship between micro and group-level causal discovery assumptions. We investigate the conditions under which assumptions like Causal Faithfulness hold or fail to hold. Our analysis encompasses graphical causal models that contain cycles and bidirected edges. We also discuss grouped time series causal graphs and variants thereof as special cases of our general theoretical framework. Thereby, we aim to provide researchers with a solid theoretical foundation for the development and application of causal discovery methods for variable groups.