用傅里叶加速的预条件加性高斯过程，显著提升大规模预测效率。
Preconditioned Additive Gaussian Processes with Fourier Acceleration
- 通过NFFT实现核矩阵乘法近线性复杂度
- 加性核分解低维特征交互，适配高维数据
- 预条件策略加速超参数调优，适合大规模不确定性建模
高斯过程（GPs）在机器学习中用于量化预测不确定性，但其由核函数定义的协方差矩阵通常稠密且规模大，带来重大计算挑战。本文提出一种无矩阵方法，利用非等距快速傅里叶变换（NFFT），在预定精度下实现核矩阵及其导数与向量乘法的近似线性复杂度。为应对高维问题，提出加性核方法，各子核捕捉低阶特征交互，使NFFT可高效应用，并在多个真实数据集上提升准确性。此外，引入预条件策略加速超参数调优，进一步提升高斯过程的效率与效果。
原文摘要 · Abstract (English)
Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant computational challenges. This paper introduces a matrix-free method that utilizes the Non-equispaced Fast Fourier Transform (NFFT) to achieve nearly linear complexity in the multiplication of kernel matrices and their derivatives with vectors for a predetermined accuracy level. To address high-dimensional problems, we propose an additive kernel approach. Each sub-kernel in this approach captures lower-order feature interactions, allowing for the efficient application of the NFFT method and potentially increasing accuracy across various real-world datasets. Additionally, we implement a preconditioning strategy that accelerates hyperparameter tuning, further improving the efficiency and effectiveness of GPs.
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