  We present a noise-injected version of the Expectation-Maximization (EM)
algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM
algorithm uses noise to speed up the convergence of the EM algorithm. The NEM
theorem shows that injected noise speeds up the average convergence of the EM
algorithm to a local maximum of the likelihood surface if a positivity
condition holds. The generalized form of the noisy expectation-maximization
(NEM) algorithm allow for arbitrary modes of noise injection including adding
and multiplying noise to the data.
  We demonstrate these noise benefits on EM algorithms for the Gaussian mixture
model (GMM) with both additive and multiplicative NEM noise injection. A
separate theorem (not presented here) shows that the noise benefit for
independent identically distributed additive noise decreases with sample size
in mixture models. This theorem implies that the noise benefit is most
pronounced if the data is sparse. Injecting blind noise only slowed
convergence.
