Cluster-Specific Variable Selection for Product Partition Models

We propose a random partition model that implements prediction with many candidate covariates and interactions. The model is based on a modified product partition model that includes a regression on covariates by favouring homogeneous clusters in terms of these covariates. Additionally, the model allows for a cluster-specific choice of the covariates that are included in this evaluation of homogeneity. The variable selection is implemented by introducing a set of cluster-specific latent indicators that include or exclude covariates. The proposed model is motivated by an application to predicting mortality in an intensive care unit in Lisboa, Portugal.