Title: Bayesian functional principal components analysis via variational message passing
Authors: Tui Nolan - University of Cambridge (United Kingdom) [presenting]
Jeff Goldsmith - Columbia University (United States)
David Ruppert - Cornell University (United States)
Abstract: Standard approaches for functional principal components analysis rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal eigenfunctions representing the major modes of variation in a set of functional data. This approach can be a computationally intensive procedure, especially in the presence of large datasets with irregular observations. We outline a variational Bayesian approach, which aims to determine the Karhunen-Loeve decomposition directly without smoothing and estimating a covariance surface. More specifically, we incorporate the notion of variational message passing over a factor graph because it removes the need for rederiving approximate posterior density functions if there is a change in the model. Instead, model changes are handled by changing specific computational units, known as fragments, within the factor graph. Indeed, this is the first method to address a functional data model via variational message passing. Our approach introduces two new fragments that are necessary for Bayesian functional principal components analysis. We present the computational details, a set of simulations for assessing the accuracy and speed of the variational message passing algorithm and an application to the United States temperature data.