Variational Bayes for Gaussian Factor Models under the Cumulative Shrinkage Process

TL;DR

This paper introduces a variational inference algorithm for Gaussian factor models with a cumulative shrinkage process, achieving comparable accuracy to adaptive Gibbs sampling but with faster computation.

Contribution

It develops a variational algorithm for Gaussian factor models with cumulative shrinkage, improving efficiency over existing Gibbs sampling methods.

Findings

The variational algorithm matches Gibbs sampler inference accuracy.

It significantly reduces computational runtime.

The method effectively induces sparse, parsimonious models.

Abstract

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 effective 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 Gaussian 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