I'm a bit confused about the E step on the EM derivation for a mixture of multinomials. I don't think I'm all the way there, but I'm confused about how to proceed. Is the E step, solving for tau? Or is it something else?
In general, what are the steps? (This is what I think the steps are).
- Setup the log likelihood.
- Realize the sum is inside log so we want to simplify some other way.
- Realize that we need a latent z variable so we have to factor that in.
- Multiply by p(z,x|u)/p(z,x|u) (effectively 1, so not changing the value).
- Rearrange so we can use Jensen's inequality to move the sum out of the log.
- .... ????? Is this result the e step?
Below is where I am so far.