An implementation of Variational LDA. See the related blogger blogpost for the details of how the formulas were derived. But in a nutshell.

Sorry for the LaTeX jargon! I wish github could render the formulas. To produce a PDF version of this file, try this command:

pandoc -t latex -o README.pdf README.md

1. For k = 1 .. K:
   1. ${\phi }_k\sim {\text{Dirichlet}}_V(\beta )$
2. For m = 1..M:
   1. ${\theta }_m\sim {\text{Dirichlet}}_K(\alpha )$
   2. For n = 1 .. N_m:
      1. $z_{mn}\sim {\text{Multinomial}}_K({\theta }_m)$
      2. $w_{mn} \sim \hbox{Multinomial}V(\sum{i=1}^KZ_{mni}\varphi_i)$

1. For m=1..M, n=1..N, k=1..K
   1. $p_{z_{mnk}}=1/k$
2. Repeat
   1. For k=1..K, v=1..V
      1. ${\beta }_{{\phi }_{kv}}=\beta +\sum _{m=1}^M\sum _{n=1}^N{w}_{mnv}{p}_{z_{mnk}}$
   2. For m=1..M, k=1..K
      1. ${\alpha }_{{\theta }_{mk}}=\alpha +\sum _{n=1}^N{p}_{z_{mnk}}$
   3. For m=1..M, n=1..N, k=1..K
      1. $p_{z_{mnk}}=\exp (\psi ({\alpha }_{{\theta }_{mk}})-\psi \left(\sum _{k^{\prime }=1}^K{\alpha }_{{\theta }_{m{k}^{\prime }}}\right)+\sum _{v=1}^V{w}_{mnv}(\psi ({\beta }_{{\phi }_{kv}})-\psi \left(\sum _{k^{\prime }=1}^K{\beta }_{{\phi }_{k^{\prime }v}}\right)))$