Space alternating data augmentation: application to finite mixture of Gaussians and speaker recognition

The SAGE (space-alternating generalized expectation-maximization) algorithm (Celeux, G. et al., 2001) is one of the most elegant and popular extensions of the EM (expectation maximization) algorithm for performing ML (maximum likelihood) or MAP (maximum a posteriori) parameter estimation. This algorithm updates parameter components by subblocks by alternating missing data spaces. Its efficiency has been reported in numerous simulation studies. We propose here an MCMC (Markov chain Monte Carlo) strategy named SADA (space-alternating data augmentation) which relies on the same principle in order to sample efficiently from (posterior) distributions and we discuss its application to finite mixtures of Gaussians. For this model, we also present an original implementation of the SAGE algorithm. In Monte Carlo simulations and in an application for speaker recognition, these methods, which are straightforward modifications of the standard EM and DA (data augmentation) algorithms, consistently outperform them.