标题： 预处理的加性高斯过程与傅里叶加速 显示英文标题

标题： Preconditioned Additive Gaussian Processes with Fourier Acceleration

摘要： 高斯过程（GPs）在机器学习中对于量化预测中的不确定性至关重要。然而，由核函数定义的其相关协方差矩阵通常是密集且大规模的，带来了显著的计算挑战。本文介绍了一种无矩阵方法，利用非均匀快速傅里叶变换（NFFT）在预先确定的精度水平下实现核矩阵及其导数与向量相乘的近线性复杂度。为了解决高维问题，我们提出了加性核方法。该方法中的每个子核捕获低阶特征交互，允许高效应用NFFT方法，并可能提高各种真实世界数据集上的准确性。此外，我们还实施了一种预处理策略以加速超参数调优，进一步提高了高斯过程的效率和有效性。 显示英文摘要

摘要： 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.