Towards Unbiased Random Features with Lower Variance For Stationary Indefinite Kernels

TL;DR

This paper introduces generalized orthogonal random features that provide unbiased kernel approximation with lower variance, improving classification and regression performance for stationary indefinite kernels.

Contribution

It proposes a novel unbiased random feature method with reduced variance for stationary indefinite kernels, outperforming existing approximation techniques.

Findings

Lower variance and approximation error compared to existing methods.

Improved classification accuracy and regression performance.

Effective for various datasets and kernel types.

Abstract

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.