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.

翻译：在大规模回归问题中，随机傅里叶特征通过从核函数的谱密度定义核函数，并利用有限蒙特卡洛样本构建近似低秩高斯过程，显著提升了高斯过程的计算可扩展性与灵活性。然而，随机傅里叶特征在核近似与贝叶斯核学习中的有效性，取决于谱测度的可采样性及生成样本的质量。本文提出斯坦随机特征方法，该方法利用斯坦变分梯度下降技术，既能生成已知谱密度的高质量随机傅里叶特征样本，又能灵活高效地逼近传统非解析的谱测度后验分布。斯坦随机特征仅需计算对数概率梯度即可执行核近似与贝叶斯核学习，其性能优于传统方法。我们通过核近似及经典高斯过程回归问题的基线对比实验，实证验证了斯坦随机特征的有效性。