# Functional Bayesian Networks for Discovering Causality from Multivariate Functional Data

arXiv: https://arxiv.org/abs/2210.12832 · HTML: https://mlsanity.com/paper/2210.12832/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2022.

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

- [Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data](https://mlsanity.com/paper/2310.20537/) (2023)
- [Functional Linear Non-Gaussian Acyclic Model for Causal Discovery](https://mlsanity.com/paper/2401.09641/) (2024)
- [Consistent Bayesian causal discovery for structural equation models with equal error variances](https://mlsanity.com/paper/2509.15197/) (2025)
- [Functional Causal Discovery via Conditional Covariance Ordering](https://mlsanity.com/paper/2609.27256/) (2026)

## Abstract (arXiv)

Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest, which has not yet been fully explored. In this article, we develop a novel Bayesian network model for multivariate functional data where the conditional independence and causal structure are both encoded by a directed acyclic graph. Specifically, we allow the functional objects to deviate from Gaussian process, which is adopted by most existing functional data analysis models. The more reasonable non-Gaussian assumption is the key for unique causal structure identification even when the functions are measured with noises. A fully Bayesian framework is designed to infer the functional Bayesian network model with natural uncertainty quantification through posterior summaries. Simulation studies and real data examples are used to demonstrate the practical utility of the proposed model.