Bayesian Multi-Group Functional Factor Models with Parameter-Expanded Cumulative Shrinkage Priors

2026-04-01

AI Summary

This study addresses the joint modeling of shared and group-specific latent structures in multi-group functional data by proposing a Bayesian multi-group functional factor analysis framework. The method employs B-spline basis expansions to obtain low-rank representations of functional observations and incorporates a parameter-expanded cumulative shrinkage prior to adaptively infer the number of shared and group-specific factors. In simulation studies, the proposed model accurately recovers the true underlying factor structure. When applied to EEG data, it successfully identifies both common and distinct neural activity patterns between individuals with alcohol dependence and healthy controls, demonstrating its effectiveness and interpretability in analyzing complex functional data.

Abstract

Functional data consist of trajectories observed over a continuous domain, such as time, space, or wavelength. Here we consider curves observed on different groups of subjects and propose a Bayesian multi-group functional factor analysis framework that jointly models the data via an explicit decomposition into group-specific mean functions and latent components that capture both common and distinct latent structures across the groups. We represent these functional components as linear combinations of a common set of B-spline bases, achieving a low-rank representation of the latent factors. We further impose a parameter-expanded cumulative shrinkage process prior on the factor loadings, which induces increasing shrinkage and automatically selects the number of active shared and group-specific factors. We evaluate the model's performance through simulation studies and show that the model accurately recovers the number of underlying factors and effectively distinguishes variations in functional observations driven by shared versus group-specific complex structures under various scenarios. For real data analysis, we apply the model to EEG data on alcoholic and healthy subjects and identify shared latent factors, that capture canonical characteristic components of the EEG curves, along with group-specific factors that reveal specific neural activity patterns.

Problem

• functional data
• multi-group
• latent factors
• factor selection
• Bayesian modeling

Innovation

• Bayesian functional factor analysis
• multi-group modeling
• cumulative shrinkage prior
• B-spline basis
• automatic factor selection