Editing Expectation–maximization algorithm (section)

=== The EM algorithm ===
The EM algorithm seeks to find the maximum likelihood estimate of the marginal likelihood by iteratively applying these two steps:
:''Expectation step (E step)'': Define <math>Q(\boldsymbol\theta\mid\boldsymbol\theta^{(t)})</math> as the [[expected value]] of the log [[likelihood function]] of <math>\boldsymbol\theta</math>, with respect to the current [[conditional probability distribution|conditional distribution]] of <math>\mathbf{Z}</math> given <math>\mathbf{X}</math> and the current estimates of the parameters <math>\boldsymbol\theta^{(t)}</math>:
::<math>Q(\boldsymbol\theta\mid\boldsymbol\theta^{(t)}) = \operatorname{E}_{\mathbf{Z} \sim p(\cdot | \mathbf{X},\boldsymbol\theta^{(t)})}\left[ \log p (\mathbf{X},\mathbf{Z} | \boldsymbol\theta) \right] \,</math>

:''Maximization step (M step)'': Find the parameters that maximize this quantity:
::<math>\boldsymbol\theta^{(t+1)} = \underset{\boldsymbol\theta}{\operatorname{arg\,max}} \ Q(\boldsymbol\theta\mid\boldsymbol\theta^{(t)}) \, </math>

More succinctly, we can write it as one equation:<math display="block">\boldsymbol\theta^{(t+1)} = \underset{\boldsymbol\theta}{\operatorname{arg\,max}} 
\operatorname{E}_{\mathbf{Z} \sim p(\cdot | \mathbf{X},\boldsymbol\theta^{(t)})}\left[ \log p (\mathbf{X},\mathbf{Z} | \boldsymbol\theta) \right] \, </math>