I am having trouble finding the correlation between the two seemingly uncorrelated parts of LDA.
What I understood from several videos is:
There is a document generation "part", which is the construction of two dirichlet distrubutions, one describing the distribution of documents to topics, and one describing the distirbution of topics to words.
There is the Gibbs sampling optimization "part", which takes in documents whose words have been assigned to topics, and at each iteration of the optimization the Gibbs sampling takes a step towards a somewhat monistic distribution of documents to topics and words to topics, i.e each document's word's belong more or less to the same topic, and each instance of a word in the corpus of documents belongs more or less to one topic.
My question is why is the first part needed? I assume its importance may be that the initial random assignment of topics need be from a dirichlet distribution, but I am not sure if it is the case.
Is there anything I am missing?