  Factors models are routinely used to analyze high-dimensional data in both
single-study and multi-study settings. Bayesian inference for such models
relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the
number of studies, observations, or measured variables increase. To address
this issue, we propose variational inference algorithms to approximate the
posterior distribution of Bayesian latent factor models using the
multiplicative gamma process shrinkage prior. The proposed algorithms provide
fast approximate inference at a fraction of the time and memory of MCMC-based
implementations while maintaining comparable accuracy in characterizing the
data covariance matrix. We conduct extensive simulations to evaluate our
proposed algorithms and show their utility in estimating the model for
high-dimensional multi-study gene expression data in ovarian cancers. Overall,
our proposed approaches enable more efficient and scalable inference for factor
models, facilitating their use in high-dimensional settings. An R package
VIMSFA implementing our methods is available on GitHub
(github.com/blhansen/VI-MSFA).
