用神经特征映射加速高斯过程推理，精度与效率双提升
Scalable Gaussian process inference via neural feature maps
- 通过神经网络学习特征映射构建表达性强核函数
- 在基准数据集上实现更高精度和更快训练预测速度
- 支持表格、图像等多模态数据，无需复杂预处理
我们提出一个理论严谨的高斯过程框架，利用神经特征映射构建表达能力强的核函数。我们证明学习到的特征映射可视为隐式再生核希尔伯特空间（RKHS）中格拉姆矩阵的最优低秩近似，从而建立高斯过程后验的一致性。进一步分析了诱导核的谱特性，并引入乘积特征映射核以缓解过平滑问题。该方法简单而强大，可在极少前期工作下实现快速、可扩展且精确的高斯过程推断。核函数设计灵活，可无缝应用于回归与分类任务，覆盖表格数据及图像等结构化领域。在多个基准数据集上，该方法在准确率以及训练和预测效率方面均优于现有方法。
原文摘要 · Abstract (English)
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix derived from an implied RKHS, from which we establish consistency of the GP posterior. We further analyse the spectral properties of the induced kernels and introduce product feature-map kernels to address oversmoothing. This simple yet powerful approach enables fast, scalable, and accurate exact GP inference with minimal upfront work. The flexibility of kernel design supports seamless application to both regression and classification tasks across diverse data modalities, including tabular inputs and structured domains such as images. On benchmark datasets, this approach surpasses pre-existing methods in terms of accuracy and training and prediction efficiency.
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