Bayesian Functional Graphical Models with Change-Point Detection

TL;DR

This paper introduces a Bayesian functional graphical model with change-point detection for analyzing time-varying connectivity in functional data, demonstrating superior graph selection and revealing meaningful dynamic patterns in ocean temperature data.

Contribution

It presents a novel Bayesian model that jointly detects change-points and infers dynamic connectivity patterns in functional data, with efficient computation and improved accuracy.

Findings

Excellent graph selection performance in simulations

Effective detection of graph change-points

Revealed meaningful ocean temperature connectivity patterns

Abstract

Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional dependencies) among multiple functions or time series. For this task, a dynamic and Bayesian functional graphical model is introduced. The proposed modeling approach prioritizes the careful definition of an appropriate graph to identify both time-invariant and time-varying connectivity patterns. A novel block-structured sparsity prior is paired with a finite basis expansion, which together yield effective shrinkage and graph selection with efficient computations via a Gibbs sampling algorithm. Crucially, the model includes (one or more) graph changepoints, which are learned jointly with all model parameters and incorporate graph dynamics. Simulation studies demonstrate excellent graph selection capabilities, with significant improvements over competing methods. The proposed approach is applied to study of dynamic connectivity patterns of sea surface temperatures in the Pacific Ocean and reveals meaningful edges.