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

TL;DR

This paper introduces a Bayesian multi-group functional factor analysis model that decomposes functional data into shared and group-specific components, automatically selecting the number of factors using a shrinkage prior.

Contribution

The proposed model uniquely combines a low-rank B-spline basis representation with a parameter-expanded cumulative shrinkage prior for automatic factor selection across groups.

Findings

Accurately recovers the true number of underlying factors in simulations.

Effectively distinguishes shared versus group-specific variations.

Identifies meaningful neural activity patterns in EEG 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.