So I was reviewing the E-step for the Gaussian Mixture model on Wikipedia.
And it looks like in the E-step all you really need to compute is the conditional distribution of Z because that is all that the M-step uses. However in the definition of the EM algorithm it states that in the E-step the Q function must be computed (i.e. the expected log likelihood)? Why doesn't it just say the conditional distribution of Z needs to be computed?
I just noticed that it also says in the article "Speaking of an expectation (E) step is a bit of a misnomer. What are calculated in the first step are the fixed, data-dependent parameters of the function Q. Once the parameters of Q are known, it is fully determined and is maximized in the second (M) step of an EM algorithm." So perhaps the answer is that it is just a misnomer i.e. it is not necessary to compute the full expected value.