A Bayesian Latent Factor Model for Functional Data

In this paper, we propose a novel Bayesian functional latent factor model that combines nonparametric latent factor modeling with functional principal component analysis to infer a parsimonious set of factors. The proposed model represents each subject’s continuous curve as a linear combination of basis functions with the corresponding coeffi- cients interpreted as factor loadings. We impose a cumulative shrinkage process prior on these basis coefficients, inducing increasing shrinkage on higher-index factors and effectively removing redundant columns in the factor loadings matrix. We evaluate the proposed methodology on both simulated functional data and a Canadian temperature dataset, showing its ability to effectively capture primary variations across subjects using a reduced set of factors.