Functional Bayesian Networks for Discovering Causality from Multivariate Functional Data

TL;DR

This paper introduces a Bayesian network model for multivariate functional data that captures causal relationships and accounts for non-Gaussian functional deviations, enabling more accurate causal inference with uncertainty quantification.

Contribution

It develops a novel Bayesian network framework for multivariate functional data that allows non-Gaussian deviations and provides a fully Bayesian inference method.

Findings

Effective in identifying causal structures in simulated data

Demonstrates practical utility on real-world datasets

Provides uncertainty quantification for causal inference

Abstract

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.