• Corpus ID: 10778991

# Relative Error Embeddings of the Gaussian Kernel Distance

@inproceedings{Chen2017RelativeEE,
title={Relative Error Embeddings of the Gaussian Kernel Distance},
author={Di Chen and J. M. Phillips},
booktitle={ALT},
year={2017}
}
• Published in ALT 17 February 2016
• Computer Science
A reproducing kernel can define an embedding of a data point into an infinite dimensional reproducing kernel Hilbert space (RKHS). The norm in this space describes a distance, which we call the kernel distance. The random Fourier features (of Rahimi and Recht) describe an oblivious approximate mapping into finite dimensional Euclidean space that behaves similar to the RKHS. We show in this paper that for the Gaussian kernel the Euclidean norm between these mapped to features has $(1+\epsilon… 9 Citations ## Figures from this paper Relative Error RKHS Embeddings for Gaussian Kernels • Computer Science ArXiv • 2018 The main insight is to effectively modify the well-traveled random Fourier features to be slightly biased and have higher variance, but so they can be defined as a convolution over the function space. The GaussianSketch for Almost Relative Error Kernel Distance • Computer Science APPROX-RANDOM • 2020 We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and N ov 2 01 8 Relative Error RKHS Embeddings for Gaussian Kernels • Computer Science • 2018 The main insight is to effectively modify the well-traveled random Fourier features to be slightly biased and have higher variance, but so they can be defined as a convolution over the function space. Fourier Sparse Leverage Scores and Approximate Kernel Learning • Computer Science NeurIPS • 2020 New explicit upper bounds on the leverage scores of Fourier sparse functions under both the Gaussian and Laplace measures are proved, which generalize existing work that only applies to uniformly distributed data. Provably Useful Kernel Matrix Approximation in Linear Time • Computer Science ArXiv • 2016 We give the first algorithms for kernel matrix approximation that run in time linear in the number of data points and output an approximation which gives provable guarantees when used in many Sketched MinDist • Computer Science SoCG • 2020 This paper shows how large this set of sketch vectors needs to be under a variety of shapes and scenarios and provides direct connection to the sensitivity sample framework, so relative error can be preserved in$d$dimensions using Q = O(d/\varepsilon^2)$.
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