Noisy Expectation-Maximization: Applications and Generalizations
This addresses the problem of slow convergence in EM algorithms for practitioners in statistics and machine learning, though it is incremental as it builds on the standard EM method.
The paper introduces the Noisy Expectation-Maximization (NEM) algorithm, which uses injected noise to speed up convergence of the EM algorithm to a local maximum of the likelihood surface under a positivity condition, demonstrating benefits on Gaussian mixture models with additive and multiplicative noise.
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.