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)} $
Contents
hide
Best Answer
It looks like Bayes' formula :
$Pr[A mid B] = frac{Pr[B mid A] Pr[A]}{Pr[B]}$
Here, it gives: $Pr[X mid z, theta] = frac{Pr[z mid X, theta] Pr[X mid theta]}{Pr[z mid theta]}$