  The Expectation Maximization (EM) algorithm is widely used as an iterative
modification to maximum likelihood estimation when the data is incomplete. We
focus on a semi-supervised case to learn the model from labeled and unlabeled
samples. Existing work in the semi-supervised case has focused mainly on
performance rather than convergence guarantee, however we focus on the
contribution of the labeled samples to the convergence rate. The analysis
clearly demonstrates how the labeled samples improve the convergence rate for
the exponential family mixture model. In this case, we assume that the
population EM (EM with unlimited data) is initialized within the neighborhood
of global convergence for the population EM that consists solely of samples
that have not been labeled. The analysis for the labeled samples provides a
comprehensive description of the convergence rate for the Gaussian mixture
model. In addition, we extend the findings for labeled samples and offer an
alternative proof for the population EM's convergence rate with unlabeled
samples for the symmetric mixture of two Gaussians.
