Editing Expectation–maximization algorithm (section)

=== The symbols ===
Given the [[statistical model]] which generates a set <math>\mathbf{X}</math> of observed data, a set of unobserved latent data or [[missing values]] <math>\mathbf{Z}</math>, and a vector of unknown parameters <math>\boldsymbol\theta</math>, along with a [[likelihood function]] <math>L(\boldsymbol\theta; \mathbf{X}, \mathbf{Z}) = p(\mathbf{X}, \mathbf{Z}\mid\boldsymbol\theta)</math>, the [[maximum likelihood estimate]] (MLE) of the unknown parameters is determined by maximizing the [[marginal likelihood]] of the observed data

:<math>L(\boldsymbol\theta; \mathbf{X}) = p(\mathbf{X}\mid\boldsymbol\theta) = \int  p(\mathbf{X},\mathbf{Z} \mid \boldsymbol\theta) \, d\mathbf{Z} = \int  p(\mathbf{X} \mid \mathbf{Z}, \boldsymbol\theta) p(\mathbf{Z} \mid \boldsymbol\theta) \, d\mathbf{Z} </math>

However, this quantity is often intractable since <math>\mathbf{Z}</math> is unobserved and the distribution of <math>\mathbf{Z}</math> is unknown before attaining <math>\boldsymbol\theta</math>.