I've seen this paper's straightforward description of the EM algorithm cited countless times now to explain EM (figure below). But it's only causing me more confusion because I have trouble seeing how it aligns with EM theory.
In theory, the M step of EM is about finding the $\theta$ values that maximize the expectation of the log likelihood, given the current guess of parameters. However, this paper does not seem to calculate the expectation of the log likelihood at all. Instead, it multiplies the heads & tails counts with normalized likelihoods of coin A and coin B.
Am I missing something? Is it proven somewhere that for this particular model, this procedure maximizes the expectation of the log likelihood, and it's just not shown in the paper? I'm having a lot of trouble reconciling the EM algorithm with this very straightforward example.