  Thanks to the reparameterization trick, deep latent Gaussian models have
shown tremendous success recently in learning latent representations. The
ability to couple them however with nonparamet-ric priors such as the Dirichlet
Process (DP) hasn't seen similar success due to its non parameteriz-able
nature. In this paper, we present an alternative treatment of the variational
posterior of the Dirichlet Process Deep Latent Gaussian Mixture Model
(DP-DLGMM), where we show that the prior cluster parameters and the variational
posteriors of the beta distributions and cluster hidden variables can be
updated in closed-form. This leads to a standard reparameterization trick on
the Gaussian latent variables knowing the cluster assignments. We demonstrate
our approach on standard benchmark datasets, we show that our model is capable
of generating realistic samples for each cluster obtained, and manifests
competitive performance in a semi-supervised setting.
