Bayesian Functional Principal Components Analysis via Variational Message Passing with Multilevel Extensions

Standard approaches for functional principal components analysis rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal eigenfunctions representing major modes variation set data. This approach can be computationally intensive procedure, especially presence large datasets with irregular observations. In this article, we develop variational Bayesian approach, which aims determine Karhunen-Loève decomposition directly without smoothing and estimating surface. More specifically, incorporate notion message passing over factor graph because it removes need rederiving approximate posterior density functions if there is change model. Instead, model changes are handled by changing specific computational units, known as fragments, within – demonstrate extension multilevel Indeed, first article address data via passing. Our introduces three new fragments that necessary analysis. We present details, simulations assessing accuracy speed algorithm application United States temperature