Does the EM algorithm require i.i.d?

Question

The EM algorithm roughly has two steps.
E-Step:
Calculate the conditional expectation of the likelihood function given the data $x_1, . . . , x_n $ and the current estimates of parameters $\Theta^{[k]}$. So the objective function would be $Q(\Theta, \Theta^{[k]})=E[\ln(\Theta,x_1, . . . , x_n)|x_1, . . . , x_n,\Theta^{[k]}]$
M-step:
Maximize the objective function with respect to $\Theta $ to obtain the next set of estimates $\Theta^{[k+1]}$.

Now does the EM algorithm require i.i.d data to estimate the parameters? Is that possible to use EM algorithm even in the case of non i.i.d data?

Answer 1

What you are trying to do with EM is maximize the likelihood of a parameterized distribution according to some data.

Now the underlying assumptions on your data are reflected in the likelihood.

If the likelihood you have at hand is the product of the individual likelihoods for each data point, you implicitly made the hypothesis that the data is i.i.d. and this is indeed very common case according to my experience.

Otherwise you can totally have a likelihood that reflects interactions between data points (e.g. time series) and still use EM to maximize the likelihood, at least locally.