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Rahimi and Recht introduce randomized, explicit low-dimensional feature maps whose Euclidean inner products approximate shift-invariant kernels, allowing nonlinear kernel methods to be replaced by fast linear learning. They develop random Fourier features from a kernel's spectral distribution and random binning features from randomly shifted grids, and give uniform approximation bounds for both constructions. Using ridge regression on five large-scale regression and classification datasets, they compare the two feature families with Core Vector Machines and published exact-kernel baselines. Reported results show competitive test error with substantial, though dataset-dependent, training-time advantages, while also revealing differences between interpolation-oriented Fourier features and locality-preserving binning features.
The paper shows that a nonlinear kernel can be approximated before learning by an explicit randomized representation, making ordinary linear solvers useful on datasets for which full kernel matrices are expensive. This became a foundational route to scalable kernel learning. The reported benefits are not uniform: Fourier and binning features behave differently by task, some baselines are faster on smaller or oversampled datasets, and the KDDCUP99 comparison is unusually sensitive to ordering and regularization. The experiments support scalable approximation, not equivalence to exact kernel methods in every setting.
The paper’s claims are available in Research claims.