Noise benefits in the expectation-maximization algorithm: Nem theorems and models

We prove a general sufficient condition for a noise benefit in the expectation-maximization (EM) algorithm. Additive noise speeds the average convergence of the EM algorithm to a local maximum of the likelihood surface when the noise condition holds. The sufficient condition states when additive noise makes the signal more probable on average. The performance measure is Kullback relative entropy. A Gaussian-mixture problem demonstrates the EM noise benefit. Corollary results give other special cases when noise improves performance in the EM algorithm.