Dirk Van Gucht, Ryan Williams, et al.
SIGMOD/PODS 2015
Kernel ridge regression is a simple yet powerful technique for nonparametric regression whose computation amounts to solving a linear system. This system is usually dense and highly ill-conditioned. In addition, the dimensions of the matrix are the same as the number of data points, so direct methods are unrealistic for large-scale datasets. In this paper, we propose a preconditioning technique for accelerating the solution of the aforementioned linear system. The preconditioner is based on random feature maps, such as random Fourier features, which have recently emerged as a powerful technique for speeding up and scaling the training of kernel-based methods, such as kernel ridge regression, by resorting to approximations. However, random feature maps only provide crude approximations to the kernel function, so delivering state-of-the-art results by directly solving the approximated system requires the number of random features to be very large. We show that random feature maps can be much more effective in forming preconditioners, since under certain conditions a not-too-large number of random features is sufficient to yield an effective preconditioner. We empirically evaluate our method and show it is highly effective for datasets of up to one million training examples.
Dirk Van Gucht, Ryan Williams, et al.
SIGMOD/PODS 2015
Petros Drineas, Malik Magdon-Ismail, et al.
JMLR
Kenneth L. Clarkson, David P. Woodruff
Journal of the ACM
Moritz Hardt, David P. Woodruff
STOC 2013