# Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data

arXiv: https://arxiv.org/abs/2310.20537 · HTML: https://mlsanity.com/paper/2310.20537/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 53 references that are in the map.
- First posted on arXiv 31 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Cyclic Causal Discovery from Continuous Equilibrium Data](https://mlsanity.com/paper/1309.6849/) (2013)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Causal Discovery with Heterogeneous Observational Data](https://mlsanity.com/paper/2201.12392/) (2022)
- [Bayesian cumulative shrinkage for infinite factorizations](https://mlsanity.com/paper/1902.04349/) (2019)
- [Bayesian Graphical Models for Multivariate Functional Data](https://mlsanity.com/paper/1411.4158/) (2014)
- [Multivariate Functional Additive Mixed Models](https://mlsanity.com/paper/2103.06606/) (2021)
- [Functional Bayesian Networks for Discovering Causality from Multivariate Functional Data](https://mlsanity.com/paper/2210.12832/) (2022)
- [A Bayesian Multivariate Functional Dynamic Linear Model](https://mlsanity.com/paper/1411.0764/) (2014)
- [A functional regression model for heterogeneous BioGeoChemical Argo data in the Southern Ocean](https://mlsanity.com/paper/2211.04012/) (2022)

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

- [Functional Linear Non-Gaussian Acyclic Model for Causal Discovery](https://mlsanity.com/paper/2401.09641/) (2024)
- [A method to benchmark high-dimensional process drift detection](https://mlsanity.com/paper/2409.03669/) (2024)
- [Towards Privacy-Aware Bayesian Networks: A Credal Approach](https://mlsanity.com/paper/2509.18949/) (2025)
- [Functional Causal Discovery via Conditional Covariance Ordering](https://mlsanity.com/paper/2609.27256/) (2026)

## Abstract (arXiv)

Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when the underlying graph involving the multivariate functions may have cycles. To enhance interpretability, our model involves a low-dimensional causal embedded space such that all the relevant causal information in the multivariate functional data is preserved in this lower-dimensional subspace. We prove that the proposed model is causally identifiable under standard assumptions that are often made in the causal discovery literature. To carry out inference of our model, we develop a fully Bayesian framework with suitable prior specifications and uncertainty quantification through posterior summaries. We illustrate the superior performance of our method over existing methods in terms of causal graph estimation through extensive simulation studies. We also demonstrate the proposed method using a brain EEG dataset.