Latent Dirichlet allocation 297
Clearly, the equation inside the integration has the same form as the Dirichlet distribution. According to the Dirichlet
distribution,Thus,
Now we turn our attentions to the part. Actually, the derivation of the part is very similar to the part. Here
we only list the steps of the derivation:For clarity, here we write down the final equation with both and integrated out:
The goal of Gibbs Sampling here is to approximate the distribution of. Since is
invariable for any of Z, Gibbs Sampling equations can be derived from directly. The key point is
to derive the following conditional probability: