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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.

enter image description here

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

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