Random Fourier Features

K-DSN

深度堆叠网络

Random Features for Large-Scale Kernel Machines

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. Our randomized 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 algorithms that use these features outperform state-of-the-art large-scale

kernel machines.

On the Error of Random Fourier Features

https://www.cs.cmu.edu/~dsutherl/papers/rff_uai15.pdf

Kernel methods give powerful, flexible, and the-

oretically grounded approaches to solving many

problems in machine learning. The standard ap-

proach, however, requires pairwise evaluations

of a kernel function, which can lead to scalabil-

ity issues for very large datasets. Rahimi and

Recht (2007) suggested a popular approach to

handling this problem, known as random Fourier

features. The quality of this approximation, how-

ever, is not well understood. We improve the uni-

form error bound of that paper, as well as giving

novel understandings of the embedding’s vari-

ance, approximation error, and use in some ma-

chine learning methods. We also point out that

surprisingly, of the two main variants of those

features, the more widely used is strictly higher-

variance for the Gaussian kernel and has worse

bounds.