# latent variables in EM algorithm are assumed to be i.i.d from multinomial distribution, from what they are idependent

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?

• Yes, they are assumed to be independent from each other. – jsk Jun 14 '19 at 20:03
• 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. – jsk Jun 14 '19 at 21:18