Stein Random Feature Regression

TL;DR

This paper introduces Stein random features (SRF), a novel method leveraging Stein variational gradient descent to generate high-quality spectral samples for kernel approximation and Bayesian kernel learning, improving scalability and performance.

Contribution

The paper presents SRF, a new approach that efficiently approximates spectral measures for kernels, enabling better kernel learning and regression in large-scale problems.

Findings

SRF outperforms traditional RFFs in kernel approximation accuracy.

SRF achieves superior results in Gaussian process regression tasks.

SRF requires only gradient evaluations, simplifying implementation.

Abstract

In large-scale regression problems, random Fourier features (RFFs) have significantly enhanced the computational scalability and flexibility of Gaussian processes (GPs) by defining kernels through their spectral density, from which a finite set of Monte Carlo samples can be used to form an approximate low-rank GP. However, the efficacy of RFFs in kernel approximation and Bayesian kernel learning depends on the ability to tractably sample the kernel spectral measure and the quality of the generated samples. We introduce Stein random features (SRF), leveraging Stein variational gradient descent, which can be used to both generate high-quality RFF samples of known spectral densities as well as flexibly and efficiently approximate traditionally non-analytical spectral measure posteriors. SRFs require only the evaluation of log-probability gradients to perform both kernel approximation and Bayesian kernel learning that results in superior performance over traditional approaches. We empirically validate the effectiveness of SRFs by comparing them to baselines on kernel approximation and well-known GP regression problems.