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The cumulative shrinkage process is an increasing shrinkage prior that can beemployed within models in which additional terms are supposed to play aprogressively negligible role. A natural application is to Gaussian factormodels, where such a process has proved effective in inducing parsimoniousrepresentations while providing accurate inference on the data covariancematrix. The cumulative shrinkage process came with an adaptive Gibbs samplerthat tunes the number of latent factors throughout iterations, which makes itfaster than the non-adaptive Gibbs sampler. In this work we propose avariational algorithm for Gaussian factor models endowed with a cumulativeshrinkage process. Such a strategy provides comparable inference with respectto the adaptive Gibbs sampler and further reduces runtime

Variational Bayes for Gaussian Factor Models under the Cumulative Shrinkage Process