# Local Random Feature Approximations of the Gaussian Kernel

arXiv: https://arxiv.org/abs/2204.05667 · HTML: https://mlsanity.com/paper/2204.05667/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 12 Apr 2022.

## Builds on (most cited first, 6 of 6)

- [Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond](https://mlsanity.com/paper/2004.11154/) (2020)
- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017)
- [Compact Random Feature Maps](https://mlsanity.com/paper/1312.4626/) (2013)
- [Improved Random Features for Dot Product Kernels](https://mlsanity.com/paper/2201.08712/) (2022)

## Built on by (most cited first, 6 of 6)

- [Random Fourier Signature Features](https://mlsanity.com/paper/2311.12214/) (2023)
- [EUGens: Efficient, Unified, and General Dense Layers](https://mlsanity.com/paper/2601.22563/) (2026)
- [SchoenbAt: Rethinking Attention with Polynomial basis](https://mlsanity.com/paper/2505.12252/) (2025)
- [EUGens: Efficient, Unified, and General Dense Layers](https://mlsanity.com/paper/2410.09771/) (2024)
- [Multi-Hierarchical Fine-Grained Feature Mapping Driven by Feature Contribution for Molecular Odor Prediction](https://mlsanity.com/paper/2505.00290/) (2025)
- [Rationally Linearized MLPs](https://mlsanity.com/paper/2610.13568/) (2026)

## Abstract (arXiv)

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize kernel-based models by means of random feature approximations. In particular, we do so by studying a less explored random feature approximation based on Maclaurin expansions and polynomial sketches. We show that such approaches yield poor results when modelling high-frequency data, and we propose a novel localization scheme that improves kernel approximations and downstream performance significantly in this regime. We demonstrate these gains on a number of experiments involving the application of Gaussian process regression to synthetic and real-world data of different data sizes and dimensions.