提出精确分解方法，加速高维数据的高斯过程推断
Fast Gaussian process inference by exact Matérn kernel decomposition
- 通过精确分解核函数为加权累积分布，实现快速矩阵向量乘法
- 在百万级低维数据上验证，推理速度显著提升
- 适用于具有半整数平滑参数的多维Matérn核，适合科研与工程应用
为加速高斯过程推断，已有多种快速核矩阵-向量乘法（MVM）近似算法。本文基于精确核分解为加权经验累积分布函数，提出一种适用于包含半整数光滑参数多维Matérn核的精确快速MVM算法。该方法采用分治策略，将排序结果存储于数据结构中。同时提出新算法以处理固定效应预测函数。数值实验表明，该算法在包含数十万数据点的低维高斯过程问题中表现优异。代码已开源：https://gitlab.com/warin/fastgaussiankernelregression.git。
原文摘要 · Abstract (English)
To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact kernel decomposition into weighted empirical cumulative distribution functions, compatible with a class of kernels which includes multivariate Matérn kernels with half-integer smoothness parameter. This algorithm uses a divide-and-conquer approach, during which sorting outputs are stored in a data structure. We also propose a new algorithm to take into account some linear fixed effects predictor function. Our numerical experiments confirm that our algorithm is very effective for low-dimensional Gaussian process inference problems with hundreds of thousands of data points. An implementation of our algorithm is available at https://gitlab.com/warin/fastgaussiankernelregression.git.
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