A recursive sketching tree applies existing linear sketches to tensor products without forming them, giving the first oblivious subspace embeddings for high-degree polynomial and Gaussian kernels whose dimension is polynomial in the degree and independent of input dimension.
Explicit Approximations of the Gaussian Kernel
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abstract
We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the recently-proposed random Fourier features [Rahimi and Recht, 2007] in terms of the number of features, we show how this polynomial representation can provide a better approximation in terms of the computational cost involved. This makes our "Taylor features" especially attractive for use on very large data sets, in conjunction with online or stochastic training.
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Oblivious Sketching of High-Degree Polynomial Kernels
A recursive sketching tree applies existing linear sketches to tensor products without forming them, giving the first oblivious subspace embeddings for high-degree polynomial and Gaussian kernels whose dimension is polynomial in the degree and independent of input dimension.