  We propose a random feature model for approximating high-dimensional sparse
additive functions called the hard-ridge random feature expansion method
(HARFE). This method utilizes a hard-thresholding pursuit-based algorithm
applied to the sparse ridge regression (SRR) problem to approximate the
coefficients with respect to the random feature matrix. The SRR formulation
balances between obtaining sparse models that use fewer terms in their
representation and ridge-based smoothing that tend to be robust to noise and
outliers. In addition, we use a random sparse connectivity pattern in the
random feature matrix to match the additive function assumption. We prove that
the HARFE method is guaranteed to converge with a given error bound depending
on the noise and the parameters of the sparse ridge regression model. Based on
numerical results on synthetic data as well as on real datasets, the HARFE
approach obtains lower (or comparable) error than other state-of-the-art
algorithms.
