Variational Bayes for Gaussian Factor Models under the Cumulative Shrinkage Process

The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where such a process has proved effec- tive in inducing parsimonious representations while providing accurate inference on the data covariance matrix. The cumulative shrinkage process came with an adaptive Gibbs sampler that tunes the number of latent factors throughout iterations, which makes it faster than the non-adaptive Gibbs sampler. In this work we propose a variational algorithm for Gaus- sian factor models endowed with a cumulative shrinkage process. Such a strategy provides comparable inference with respect to the adaptive Gibbs sampler and further reduces runtime.