# Vector causal inference between two groups of variables

arXiv: https://arxiv.org/abs/2209.14283 · HTML: https://mlsanity.com/paper/2209.14283/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2022.

## Built on by (most cited first, 11 of 11)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (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)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Deep Learning-based Group Causal Inference in Multivariate Time-series](https://mlsanity.com/paper/2401.08386/) (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)
- [Group Interventions on Deep Networks for Causal Discovery in Subsystems](https://mlsanity.com/paper/2510.23906/) (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)

## Abstract (arXiv)

Methods to identify cause-effect relationships currently mostly assume the variables to be scalar random variables. However, in many fields the objects of interest are vectors or groups of scalar variables. We present a new constraint-based non-parametric approach for inferring the causal relationship between two vector-valued random variables from observational data. Our method employs sparsity estimates of directed and undirected graphs and is based on two new principles for groupwise causal reasoning that we justify theoretically in Pearl's graphical model-based causality framework. Our theoretical considerations are complemented by two new causal discovery algorithms for causal interactions between two random vectors which find the correct causal direction reliably in simulations even if interactions are nonlinear. We evaluate our methods empirically and compare them to other state-of-the-art techniques.