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Dirichlet Process Mixture (DPM) models have been increasingly employed tospecify random partition models that take into account possible patterns withinthe covariates. Furthermore, to deal with large numbers of covariates, methodsfor selecting the most important covariates have been proposed. Commonly, thecovariates are chosen either for their importance in determining the clusteringof the observations or for their effect on the level of a response variable(when a regression model is specified). Typically both strategies involve thespecification of latent indicators that regulate the inclusion of thecovariates in the model. Common examples involve the use of spike and slabprior distributions. In this work we review the most relevant DPM models thatinclude covariate information in the induced partition of the observations andwe focus on available variable selection techniques for these models. Wehighlight the main features of each model and demonstrate them in simulationsand in a real data application.

A comparative review of variable selection techniques for covariate dependent Dirichlet process mixture models