1. A computerized method for supervised learning by performing a Gaussian process to select and yield a set of search items to a user, comprising: receiving a set of training elements; selecting a basis element from the set of training elements; adding the basis element to a basis element set; conducting an optimization test on the basis element set with the selected basis element to produce a selection score; determining whether the selection score indicates an improvement in optimization for the basis element set; discarding the basis element if the selection score does not indicate an improvement; and retaining the basis element in the basis element set if the selection score indicates an improvement; and providing the basis element set to the Gaussian process for supervised learning to select and yield a set of search items to a user.