Integrating out θ d 's and z dn 's, the probability p(D|α, β) of the corpus is thus: Unfortunately, it is intractable to directly solve the posterior distribution of the hidden variables given a document, namely p(θ, z|w, α, β).
(Blei et al., 2003) has shown that by introducing a set of variational parameters, γ and φ, a tight lower bound on the log likelihood of the probability can be found using the following optimization procedure: γ is the Dirichlet parameter for φ and the multino- are the free variational parameters.