We introduce a normal/independent (NI) mixture model via determinantal point process (DPP), including a large class of repulsive mixture models. Extending previous works, we estimate the kernel parameters involved in DPP, which is a challenging problem. Another important problem this work addresses is finding an appropriate way to handle categorical covariates with many categories. This challenging problem in the regression model and machine learning is commonly approached representing this type of predictor through dummy variables defined for each possible level of the categorical feature. Although very popular, this strategy leads to a sparse design matrix, which can cause overfitting and produce unstable estimates for the coefficients, making the results difficult to interpret. This type of variable may also lead to poor performance of machine learning algorithms. This problem is approached by introducing a repulsive regression mixture model assuming an NI via DDP to reduce dimension and avoid overfitting for the effects of such a categorical variable. The proposed model is used to analyze simulated and real datasets.
