# Learning Structures of Bayesian Networks for Variable Groups

arXiv: https://arxiv.org/abs/1508.07753 · HTML: https://mlsanity.com/paper/1508.07753/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2015.

## Built on by (most cited first, 12 of 12)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [Typing assumptions improve identification in causal discovery](https://mlsanity.com/paper/2107.10703/) (2021)
- [Expert-Aided Causal Discovery of Ancestral Graphs](https://mlsanity.com/paper/2309.12032/) (2023)
- [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)
- [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)
- [Joint Causal Structure and Cluster Discovery Using Variational Inference](https://mlsanity.com/paper/2608.22212/) (2026)
- [Causal Preference Elicitation](https://mlsanity.com/paper/2602.01483/) (2026)
- [Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables](https://mlsanity.com/paper/2602.23611/) (2026)
- [Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria](https://mlsanity.com/paper/2610.13520/) (2026)

## Abstract (arXiv)

Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to represent different "views" to or aspects of the same entities, one may be more interested in modeling dependencies between groups of variables rather than between individual variables. Motivated by this, we study prospects of representing relationships between variable groups using Bayesian network structures. We show that for dependency structures between groups to be expressible exactly, the data have to satisfy the so-called groupwise faithfulness assumption. We also show that one cannot learn causal relations between groups using only groupwise conditional independencies, but also variable-wise relations are needed. Additionally, we present algorithms for finding the groupwise dependency structures.