Title: Mixed Deep Gaussian Mixture Models
Speaker: Denys Pommeret, Aix-Marseille University

 

Abstract:

Recently, Viroli & McLachlan (2019) proposed a generalization of the well-known  Gaussian Mixture Models (GMM) which they called Deep Gaussian Mixture Models (DGMM).  Roughly speaking, DGMMs are mixtures of GMM.  The architecture of a DGMM is that of a neural network: each mixture can be seen as a layer and its components are the neurons.  DGMMs only work  for continuous variables. Fuchs et al. (2021) proposed an extension to the mixed case (continuous and non continuous) which they call Mixed DMGG (MDGMM). 

 

The idea of a MDGMM is first to link the mixed data to a continuous latent space. Then a DGMM is applied.  The latent space contains information on the dependence structure of the mixed data. MDGMMs can be used  for clustering.

 

Another important use is data augmentation. Indeed we can modify a MDGGM to  generate mixed variables. We call this algorithm MIAMI (for MIxed data Augmentation MIxture). In this talk we show the principle of MDGMMs and we compare the MIAMI algorithm to competitors (k-modes, k-Prototypes, Hierarchical Clustering, Self-Organising Maps, DBSCAN, CTGAN, CART, Random Forest, k-Nearest Neighbour).  Finally we will evokate futur works in regression when data are unbalanced.