# Expectation Maximization (EM) The **expectation maximizatio (EM) algorithm** is a general method of finding the [[Maximum Likelihood Estimation (MLE)|maximum likelihood estimate (MLE)]] of the parameters of an underlying distribution from a given data set when the data is incomplete or has missing values (*unsupervised or semi-supervised*). 1. During the expectation step, we ## The Generalized EM Algorithm Let $\theta$ represent a vector of unknown parameters The EM algorithm seeks to find the maximum likelihood estimate (MLE) of the marginal ### The Expectation Step Let $Q(\theta | \theta^{(t)})$ be the expected ### THe Maximization Step $\theta^{(t+1)}=\underset{\theta}{\arg \max}$