Density regression using repulsive distributions

Flexible regression is a traditional motivation for the development of non-parametric Bayesian models. A popular approach for this involves a joint model for responses and covariates, from which the desired result arises by conditioning on the covariates. Many such models involve the convolution of a continuous kernel with some discrete random probability measure defined as an infinite mixture of i.i.d. atoms. Following this strategy, we propose a flexible model that involves the concept of repulsion between atoms. We show that this results in a more parsimonious representation of the regression than the i.i.d. counterpart. The key aspect is that repulsion discourages mixture components that are near each other, thus favouring parsimony. We show that the conditional model retains the repulsive features, thus facilitating interpretation of the resulting flexible regression, and with little or no sacrifice of model fit compared to the infinite mixture case. We show the utility of the methodology by way of a small simulation study and an application to a well-known data set.