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.

在大规模回归问题中，通过通过定义核函数的谱密度，利用 Monte Carlo 抽样生成有限的样本集合以形成近似的低秩高斯过程（GP），随机 Fourier 特征（RFFs）显著提高了 GP 的计算可扩展性和灵活性。然而，RFFs 在核逼近和贝叶斯核学习中的有效性取决于能否轻松地采样核谱测度并生成高质量的样本。我们引入 Stein 随机特征（SRF），利用 Stein 变分梯度下降，可以用于生成已知谱密度的高质量 RFF 样本，以及灵活高效地近似传统上非分析的谱测度后验。SRFs 只需要评估对数概率梯度，即可同时进行核逼近和贝叶斯核学习，从而在传统方法上实现更好的性能。通过将其与基准模型在核逼近和众所周知的 GP 回归问题上进行比较，我们经验证明了 SRF 的有效性。