# Quadrature-based features for kernel approximation

arXiv: https://arxiv.org/abs/1802.03832 · HTML: https://mlsanity.com/paper/1802.03832/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2018.

## Built on by (most cited first, 26 of 26)

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- [NeuralEF: Deconstructing Kernels by Deep Neural Networks](https://mlsanity.com/paper/2205.00165/) (2022)
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- [Fast Summation of Radial Kernels via QMC Slicing](https://mlsanity.com/paper/2410.01316/) (2024)
- [Gauss-Legendre Features for Gaussian Process Regression](https://mlsanity.com/paper/2101.01137/) (2021)
- [Uni-Fusion: Universal Continuous Mapping](https://mlsanity.com/paper/2303.12678/) (2023)
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- [Efficient Identification of Butterfly Sparse Matrix Factorizations](https://mlsanity.com/paper/2110.01230/) (2021)
- [Trigonometric Quadrature Fourier Features for Scalable Gaussian Process Regression](https://mlsanity.com/paper/2310.14544/) (2023)
- [Variance-Reducing Couplings for Random Features](https://mlsanity.com/paper/2405.16541/) (2024)
- [On the design of scalable, high-precision spherical-radial Fourier features](https://mlsanity.com/paper/2408.13231/) (2024)
- [Denoising Score Matching with Random Fourier Features](https://mlsanity.com/paper/2101.05239/) (2021)
- [Towards Unbiased Random Features with Lower Variance For Stationary Indefinite Kernels](https://mlsanity.com/paper/2104.06204/) (2021)
- [Arithmetic Circuits, Structured Matrices and (not so) Deep Learning](https://mlsanity.com/paper/2206.12490/) (2022)
- [Feature maps for the Laplacian kernel and its generalizations](https://mlsanity.com/paper/2502.15575/) (2025)
- [New Bounds for Kernel Sums via Fast Spherical Embeddings](https://mlsanity.com/paper/2605.01263/) (2026)
- [Fast Newton method solving KLR based on Multilevel Circulant Matrix with log-linear complexity](https://mlsanity.com/paper/2108.08605/) (2021)
- [Robust representations of oil wells' intervals via sparse attention mechanism](https://mlsanity.com/paper/2212.14246/) (2022)
- [Machine Learning Discovery of Optimal Quadrature Rules for Isogeometric Analysis](https://mlsanity.com/paper/2304.01802/) (2023)
- [Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matrices](https://mlsanity.com/paper/2408.02346/) (2024)
- [Regular Fourier Features for Nonstationary Gaussian Processes](https://mlsanity.com/paper/2602.23006/) (2026)
- [Random Fourier Features in Near-Linear Time](https://mlsanity.com/paper/2610.14751/) (2026)

## Abstract (arXiv)

We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on an efficient numerical integration technique, we propose a unifying approach that reinterprets the previous random features methods and extends to better estimates of the kernel approximation. We derive the convergence behaviour and conduct an extensive empirical study that supports our hypothesis.