The well-known fat data problem ($D»N$) is one of the main issues that Machine Learning (ML) has to deal with nowadays. For that task, we start from two different well-known models: The Bayesian linear regression (BLR) and the Relevance Vector Machines (RVM), where the first one represents the Bayesian formulation of the classic linear regression, and the second one the Bayesian formulation of support vector machines (SVM). In this paper, we propose a new model to overcome the fat problem: The Relevance Feature and Vector Machine (RFVM). RFVM combines the capabilities of the BLR model with the dual trick and the features of the RVM to introduce some new extensions to our model: (1) we work together on the primal and dual space by defining two new variables; (2) we define an Automatic Relevance Determination (ARD) over some variables by establishing sparse priors; and (3) we adapt the mathematical formula of the primal weight variable to work within a high $D$-dimension framework. We performed several experiments to test the performance of our model on real databases compared to well-known state-of-the-art models. We can state that our model can provide competitive performance with a set of well-known and commercial models.