Unsupervised Bayesian naive Bayes I'm reading a paper Gibbs sampling for the uninitiated.
In this paper, the authors try to use Gibbs sampling for a bayesian naive bayes model. They formalize the model as a graphical model in page 8. And in the example, they are trying to predict the emotion(sentiment) of a document. 
However, what I don't understand is that, they claim without label $L$, using Gibbs sampling could still sample all the parameters needed, including $L$. I'm not sure how should I interpret this. Without training label, it's essentially a clustering problem, but if not using labels, how should we interpret the learnt label $L$?
Thanks in advance.
 A: Too long for a comment.
In page 7 section 2, the authors clearly establish both labels "1" and "0" for the classes of their dataset. So, let's say "1" is "happy" and "0" is "sad". There you have your sentiment analysis.
Since they chose to use Naive Bayes as classifier, there are some parameters and hyperparameters to calculate in the Bayesian formulation. Such parameters are usually obtained integrating over all possible values (see 2.4.3). However, I think the point of this paper, is to show you that you can get away without calculating difficult integrals and instead, estimate conditional probabilities using Gibbs sampling (see 2.5.2).
At least, from what I have been able to look at, they're using labels to get an approximation of the joint distribution via Gibbs sampling.
A: Probably the questioner has got the answer, its been a long time, but the accepted answer doesn't seem to answer the question well. The unsupervised naive Bayes text classifier tries to find the most prominant classes in the data set. Those may not be the classes you are looking for. You may be looking for a happy/sad classes but the most prominent classes may be.. say.. of present/past tenses, and the sampler would find tense class only.
In order to prevent the sampler from discovering unintended classes one need to seed the sampler with labeled data.Section 2.5.3 in the paper talks about just that, however the need for using labeled data is not mentioned. This allows the sampler to get some idea of the ground truth and then generalize better using unlabeled data.
The paper "Semi-Supervised Text Classification Using EM by Kamal Nigam et.al" shows how  unsupervised learning can improve the results of supervised learning. Here the authors improve the results of supervised learning by adding to it unsupervised learning with  unlabeled data. They say if that if  the unlabeled data is much larger the performance decreases. This happens because the algorithm then drifts away to the most prominent classes in the data, not the ones you want.     
