Topic Model Gibbs Sampling Inference 步骤

1. difference between hidden variables and hyperparameter

2. procudre

step 1: the complete-data likelihood, given hyperparameter

p(w, z, theta, pi | alpha, beta)

step 2: the observed data
likelihood, given hidden variables

p(w | theta, pi)

step 3: determine which hidden variable can be integrated out, i.e. collapsed out.

theta, pi can be integrated out, thus the gibbs sampler is for p(z|w)

step 4: apply bayesian methods for
full conditional distribution p(z_i|, z_-i, w)

p(z_i| z_-i, w) = p(z,w)/{integrate z_i, p(z,w)}

step 5: based on the equation above, we need to calculate the
joint distribution of p(z,w)