Before revision:  This paper introduces the sparse random feature method that learns parsimonious random feature models utilizing techniques from compressive sensing . We provide uniform bounds on the approximation error  for functions in a  reproducing kernel Hilbert space  depending on the number of samples and the distribution of features.
After revision:  This paper introduces the sparse random feature method that learns parsimonious random feature models utilizing techniques from compressive sensing to generate random feature expansions with theoretical guarantees even in the data-scarce setting. In particular, we provide uniform bounds on the approximation error for functions in a reproducing kernel Hilbert space depending on the number of samples and the distribution of features.