# Towards Unbiased Random Features with Lower Variance For Stationary Indefinite Kernels

arXiv: https://arxiv.org/abs/2104.06204 · HTML: https://mlsanity.com/paper/2104.06204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 13 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [Quasi-Monte Carlo Feature Maps for Shift-Invariant Kernels](https://mlsanity.com/paper/1412.8293/) (2014)
- [Quadrature-based features for kernel approximation](https://mlsanity.com/paper/1802.03832/) (2018)
- [Convex Formulation for Kernel PCA and its Use in Semi-Supervised Learning](https://mlsanity.com/paper/1610.06811/) (2016)
- [Structured adaptive and random spinners for fast machine learning computations](https://mlsanity.com/paper/1610.06209/) (2016)

## Built on by (most cited first, 1 of 1)

- [Signed random Fourier features for fast density estimation with indefinite kernels](https://mlsanity.com/paper/2608.29265/) (2026)

## Abstract (arXiv)

Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could be converted to that for stationary indefinite kernels when the inputs are restricted to the unit sphere. Numerous methods provide accessible ways to approximate stationary but indefinite kernels. However, they are either biased or possess large variance. In this article, we propose the generalized orthogonal random features, an unbiased estimation with lower variance.Experimental results on various datasets and kernels verify that our algorithm achieves lower variance and approximation error compared with the existing kernel approximation methods. With better approximation to the originally selected kernels, improved classification accuracy and regression ability is obtained with our approximation algorithm in the framework of support vector machine and regression.