Variational message passing (VMP) applied to LDA

Variational Bayes (VB) applied to latent Dirichlet allocation (LDA) is the original inference mechanism for LDA. Many variants of VB for LDA, as well as for VB in general, have been developed since LDA's inception in 2013, but standard VB is still widely applied to LDA. Variational message passing (VMP) is the message passing equivalent of VB and is a useful tool for constructing a variational inference solution for a large variety of conjugate exponential graphical models (there is also a non conjugate variant available for other models). In this article we present the VMP equations for LDA and also provide a brief discussion of the equations. We hope that this will assist others when deriving variational inference solutions to other similar graphical models.