While im going through the derivation of E step in EM algorithm for pLSA, i came across the following derivation at this page. Could anyone explain me how the following step is derived.
$\sum_z q(z) log \frac{P(X|z,\theta)P(z|\theta)}{q(z)} = \sum_z q(z) log \frac{P(z|X,\theta)P(X,\theta)}{q(z)} $
Best Answer
It looks like Bayes' formula :
$\Pr[A \mid B] = \frac{\Pr[B \mid A] \Pr[A]}{\Pr[B]}$
Here, it gives: $\Pr[X \mid z, \theta] = \frac{\Pr[z \mid X, \theta] \Pr[X \mid \theta]}{\Pr[z \mid \theta]}$