This is used to learn the parameters for a Gaussian Mixture Model
We cannot simply maximise the likelihood function, because this cannot be specified for a latent model.
The log likelihood function normally is:
\(L(\theta ; X)=p(X|\theta )\)
With hidden variables it is:
\(L(\theta ; X, Z)=p(X|\theta )=\int p(X, Z|\theta)dZ\)
We consider the expected log likelihood. We call this
\(E[\log L(\theta ; X, Z)]\)