I fit EM algorithm to mixture data. Then, I would like to implement AIC for this mixture data. I really could not find a clear mathematical formula to implement AIC for mixture data when we use EM algorithm. So, based on my reading, I understand that:

$$AIC = -2\log(\hat{\theta}) + 2K$$

where K is the number of model parameters.

$$\log(\hat{\theta}) = \sum (\tau_1(\log(\pi_1)+\log(c_1(\theta))) + (\tau_2(\log(\pi_2)+\log(c_2(\theta)))$$

where $c_1$ and $c_2$ are the first and second mixture components (densities) respectively.

Is that correct? Or do I did something wrong?


1 Answer 1


The AIC in this case can be obtained from the expected log likelihood.


Use of the AIC with the EM algorithm: A demonstration of a probability model selection technique.


  • 1
    $\begingroup$ Could you expand on this answer here? It would help future readers, especially if the link goes dead. $\endgroup$
    – mkt
    Nov 8, 2017 at 4:00
  • $\begingroup$ Could you please gives further explanation. $\endgroup$
    – Silver_80
    Nov 8, 2017 at 7:53

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