information:extraction
As a maximization–maximization procedure

The EM algorithm can be viewed as two alternating maximization steps, that is, as an example of coordinate descent. Consider the function:

where q is an arbitrary probability distribution over the unobserved data z and H(q) is the entropy of the distribution q. This function can be written as

where p Z ∣ X (⋅ ∣ x; θ) {\displaystyle p_{Z\mid X}(\cdot \mid x;\theta)} is the conditional distribution of the unobserved data given the observed data x {\displaystyle x} and D K L {\displaystyle D_{KL}} is the Kullback–Leibler divergence.

Then the steps in the EM algorithm may be viewed as: