Trigonometric Quadrature Fourier Features for Scalable Gaussian Process Regression
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Abstract (arXiv)
Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in recent years due to their improved approximation accuracy and better calibrated uncertainty estimates compared to Random Fourier Feature (RFF) methods. However, a key limitation of QFF is that its performance can suffer from well-known pathologies related to highly oscillatory quadrature, resulting in mediocre approximation with limited features. We address this critical issue via a new Trigonometric Quadrature Fourier Feature (TQFF) method, which uses a novel non-Gaussian quadrature rule specifically tailored for the desired Fourier transform. We derive an exact quadrature rule for TQFF, along with kernel approximation error bounds for the resulting feature map. We then demonstrate the improved performance of our method over RFF and Gaussian QFF in a suite of numerical experiments and applications, and show the TQFF enjoys accurate GP approximations over a broad range of length-scales using fewer features.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 26 of its 63 references that are in the map. First posted on arXiv 23 Oct 2023.
Builds on
26 of 63 references.
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.