Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data

TL;DR

This paper introduces a Bayesian causal discovery method for multivariate functional data with cyclic structures, using a low-dimensional embedded space to improve interpretability and causal identifiability.

Contribution

It proposes a novel functional linear structural equation model with cycles, incorporating a low-dimensional causal space and a Bayesian inference framework for functional data.

Findings

Outperforms existing methods in causal graph estimation

Proven causal identifiability under standard assumptions

Demonstrated effectiveness on EEG dataset

Abstract

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.