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)} $

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#### Best Answer

It looks like Bayes' formula :

$Pr[A mid B] = frac{Pr[B mid A] Pr[A]}{Pr[B]}$

Here, it gives: $Pr[X mid z, theta] = frac{Pr[z mid X, theta] Pr[X mid theta]}{Pr[z mid theta]}$