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On the Error of Random Fourier Features

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arxiv 1506.02785 v1 pith:DO6A5RQC submitted 2015-06-09 cs.LG stat.ML

Danica J. Sutherland , Jeff Schneider This is my paper
classification cs.LGstat.ML
keywords errorfeatureskernelapproachapproximationfourierhoweverlearning
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Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability 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, however, is not well understood. We improve the uniform error bound of that paper, as well as giving novel understandings of the embedding's variance, approximation error, and use in some machine 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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonlinear Bias-Compensated Adaptive Filter and Its Application for Time-Series Prediction

    cs.LG 2026-07 conditional novelty 4.0 of 10

    RFFBCGA—a fixed-size random-Fourier adaptive filter with input-noise bias compensation and a general robust loss—outperforms BCKLMS and RFFMCC in nonlinear EIV time-series prediction experiments.

  2. Information-Based Exploration via Random Features for Reinforcement Learning

    cs.LG 2026-07 conditional novelty 4.0 of 10

    Random-feature Gaussian-process information gain is turned into a closed-form exploration bonus for PPO that matches RND/VIME/#Explo on 12 control, navigation, and sparse-locomotion tasks, with error bounds on the app...

  3. Random at First, Fast at Last: NTK-Guided Fourier Pre-Processing for Tabular DL

    cs.LG 2025-06 conditional novelty 3.0 of 10

    Fixed random Fourier projections on tabular inputs are claimed to bound the NTK, speed up gradient descent, and improve accuracy across four architectures and eight benchmarks.

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