On the Convergence Properties of the Mini-Batch EM and MCEM Algorithms

The EM algorithm is one of the most popular algorithm for inference in latent data models. For large datasets, each iteration of the algorithm can be numerically involved. To alleviate this problem, (Neal and Hinton, 1998) has proposed an incremental version in which the conditional expectation of the latent data (E-step) is computed on a mini-batch of observations. In this paper, we analyse this variant and propose and analyse the Monte Carlo version of the incremental EM in which the conditional expectation is evaluated by a Markov Chain Monte Carlo (MCMC). We establish the almost-sure convergence of these algorithms, covering both the mini-batch EM and its stochastic version. Various numerical applications are introduced in this article to illustrate our findings