A note on variational Bayesian factor analysis

Existing works on variational bayesian (VB) treatment for factor analysis (FA) model such as [Ghahramani, Z., & Beal, M. (2000). Variational inference for Bayesian mixture of factor analysers. In Advances in neural information proceeding systems. Cambridge, MA: MIT Press; Nielsen, F. B. (2004). Variational approach to factor analysis and related models. Master’s thesis, The Institute of Informatics and Mathematical Modelling, Technical University of Denmark.] are found theoretically and empirically to suffer two problems: ① penalize the model more heavily than BIC and ② perform unsatisfactorily in low noise cases as redundant factors can not be effectively suppressed. A novel VB treatment is proposed in this paper to resolve the two problems and a simulation study is conducted to testify its improved performance over existing treatments.