So bases of the order of thousands present no difficulties for data sets that are an order of magnitude or more bigger. Of course testing of the fit is done, generally on out-of-sample data. This protocol is not the usual split-train-test protocol. Methods based on Kernel Ridge Regression or Gaussian Process Regression are "trained" directly on a dataset and the resulting linear algebra problem, i.e., a matrix inverse of the Kernel at the configurations of the dataset, are limited to datasets of the order of thousands, much smaller than the datasets used in PIP Linear Regression.