Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data

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.

arXiv comment36 pages, 2 figures, 7 tables

References in corpus (9)

• Optimal predictive model selection
• A Widely Applicable Bayesian Information Criterion
• A Discovery Algorithm for Directed Cyclic Graphs
• A hidden spatial-temporal Markov random field model for network-based analysis of time course gene expression data
• What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective
• Cyclic Causal Discovery from Continuous Equilibrium Data
• Bayesian Graphical Models for Multivariate Functional Data
• Causal Discovery with Heterogeneous Observational Data
• A functional regression model for heterogeneous BioGeoChemical Argo data in the Southern Ocean