Expectation Maximization, E step clarification

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).

1. Setup the log likelihood.
2. Realize the sum is inside log so we want to simplify some other way.
3. Realize that we need a latent z variable so we have to factor that in.
4. Multiply by p(z,x|u)/p(z,x|u) (effectively 1, so not changing the value).
5. Rearrange so we can use Jensen's inequality to move the sum out of the log.
6. .... ????? Is this result the e step?

Below is where I am so far.

• I am confused is this a derivation that you have come up with or is it something you are trying to understand? – Chinny84 Nov 17 '14 at 14:02
• I came up with this (based on examples from Bishop's book). – William Falcon Nov 17 '14 at 15:59