Ali Rahimi coauthored Random Features for Large-Scale Kernel Machines by Ali Rahimi and Benjamin Recht in 2007. With Benjamin Recht, he proposed explicit randomized maps whose inner products approximate a chosen kernel, enabling familiar fast linear methods in the transformed feature space.[ref]
The Random Fourier feature mechanism samples frequencies from a shift-invariant kernel's spectral representation. This separates the cost of constructing a feature map from the cost of repeatedly evaluating every pairwise kernel value. Accuracy and computation depend on the feature count; randomness does not eliminate approximation error or the need to validate the learned predictor.
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