  In this work we investigate the generalization performance of random feature
ridge regression (RFRR). Our main contribution is a general deterministic
equivalent for the test error of RFRR. Specifically, under a certain
concentration property, we show that the test error is well approximated by a
closed-form expression that only depends on the feature map eigenvalues.
Notably, our approximation guarantee is non-asymptotic, multiplicative, and
independent of the feature map dimension -- allowing for infinite-dimensional
features. We expect this deterministic equivalent to hold broadly beyond our
theoretical analysis, and we empirically validate its predictions on various
real and synthetic datasets. As an application, we derive sharp excess error
rates under standard power-law assumptions of the spectrum and target decay. In
particular, we provide a tight result for the smallest number of features
achieving optimal minimax error rate.
