Section: New Results

Degeneracy in multivariate Gaussian mixtures (missing data case)

Participants : Christophe Biernacki, Vincent Vandewalle.

In the case of multivariate Gaussian mixtures, unbounded likelihood is an important theoretical and practical problem. However, in the case of missing data situations, this drawback is exacerbated for too reasons. Firstly, degeneracy frequence increases with missing data occurrence. Secondly, the EM dynamic is hardly detected since it implies linear grows of the log-likelihood, contrary to exponential grows in the complete data case, leading to computation waste and also high risk of erroneous estimates. Using the weak information that the latent sample size of each component (restricted to complete data) has to be greater than the space dimension, it is derived a simple contraint EM algorithm variant allowing to solve simultaneously both problems. This work has been presented to the international workshop [28] and a paper for an international journal is been prepared.