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In EM algorithm we introduce a latent variables, say $z_i$, $i=1,...n$, $n$ is the number of the mixture component. These variables ($z_i$) are assumed to be independent and identically distributed from multinomial distribution. My question is: from what are these variable independent?

My understanding:

$z_i$ assumed to be independent from each other. Is that correct?

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    $\begingroup$ Yes, they are assumed to be independent from each other. $\endgroup$
    – jsk
    Commented Jun 14, 2019 at 20:03
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    $\begingroup$ I think I see the confusion. You need to be careful with notation. $n$ is usually the number of individuals, not the number of mixture components. Let $z_{i}$ be a vector of 0 and 1 representing the assignment of the ith individual to one of n classes. Of course the 0's and 1's within the multinomial vector for the ith individual are not independent since only one can be a 1. They are independent across individuals. $\endgroup$
    – jsk
    Commented Jun 14, 2019 at 21:18

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