Latent Dirichlet allocation 298
where denotes the hidden variable of the word token in the document. And further we assume
that the word symbol of it is the word in the vocabulary. denotes all the s but. Note that
Gibbs Sampling needs only to sample a value for , according to the above probability, we do not need the
exact value of but the ratios among the probabilities that can take value.
So, the above equation can be simplified as:Finally, let be the same meaning as but with the excluded. The above equation can be
further simplified by treating terms not dependent on as constants:
Note that the same formula is derived in the article on the Dirichlet compound multinomial distribution, as part of a
more general discussion of integrating Dirichlet distribution priors out of a Bayesian network.