Part of Advances in Neural Information Processing Systems 20 (NIPS 2007)
Ali Rahimi, Benjamin Recht
To accelerate the training of kernel machines, we propose to map the input data to a randomized low-dimensional feature space and then apply existing fast linear methods. The features are designed so that the inner products of the transformed data are approximately equal to those in the feature space of a user speciﬁed shift- invariant kernel. We explore two sets of random features, provide convergence bounds on their ability to approximate various radial basis kernels, and show that in large-scale classiﬁcation and regression tasks linear machine learning al- gorithms applied to these features outperform state-of-the-art large-scale kernel machines.