arXiv:2503.02259cs.LG2025-03被引 6

HiGP加速高斯过程计算,让大规模数据处理更高效。

HiGP: A high-performance Python package for Gaussian Process

  • 用层次化核表示和H^2矩阵实现近线性复杂度
  • 支持在线核计算,大幅降低存储开销
  • 内置自适应预处理器,提升求解器收敛速度

高斯过程(GPs)是灵活的非参数贝叶斯模型,广泛用于回归与分类,因其能捕捉复杂数据模式并量化预测不确定性。然而,核矩阵运算的O(n³)计算成本严重限制了其在大规模数据上的应用。HiGP是一款高性能Python包,通过先进的数值线性代数和层次化核表示克服这一瓶颈。它采用H²矩阵,在空间数据上实现存储与计算的近线性复杂度;支持在大规模问题中按需计算核值,避免显式存储;集成鲁棒的自适应分解Nyström(AFN)预处理器,显著加速各类核谱下的迭代求解器收敛。核心计算以C++实现,通过Python接口提供,可无缝融入现代机器学习工作流。同时包含解析梯度计算,避免迭代求解器中自动微分的低效问题。作为可复用的数值引擎,HiGP可与GPJax、KeOps、GaussianProcesses.jl等框架协同,为大规模高斯过程回归与分类提供可靠且高效的计算支撑。

原文摘要 · Abstract (English)

Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification because of their ability to capture complex data patterns and quantify predictive uncertainty. However, the O(n^3) computational cost of kernel matrix operations poses a major obstacle to applying GPs at scale. HiGP is a high-performance Python package designed to overcome these scalability limitations through advanced numerical linear algebra and hierarchical kernel representations. It integrates H^2 matrices to achieve near-linear complexity in both storage and computation for spatial datasets, supports on-the-fly kernel evaluation to avoid explicit storage in large-scale problems, and incorporates a robust Adaptive Factorized Nyström (AFN) preconditioner that accelerates convergence of iterative solvers across a broad range of kernel spectra. These computational kernels are implemented in C++ for maximum performance and exposed through Python interfaces, enabling seamless integration with modern machine learning workflows. HiGP also includes analytically derived gradient computations for efficient hyperparameter optimization, avoiding the inefficiencies of automatic differentiation in iterative solvers. By serving as a reusable numerical engine, HiGP complements existing GP frameworks such as GPJax, KeOps, and GaussianProcesses.jl, providing a reliable and scalable computational backbone for large-scale Gaussian Process regression and classification.

高斯过程计算加速稀疏核数值优化

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