用迭代法与路径条件化，让高斯过程高效处理大规模数据。
Scalable Gaussian Processes: Advances in Iterative Methods and Pathwise Conditioning
- 结合迭代求解与路径条件化，将复杂计算转为线性方程组求解。
- 大幅降低内存消耗，支持更大规模数据处理。
- 适合需要不确定性建模的工业级大规模机器学习场景。
高斯过程是一种强大的不确定性感知函数逼近与序贯决策框架。然而，其经典形式难以在大规模数据和现代并行硬件上高效扩展，促使研究者开发多种可扩展技术。本论文聚焦于迭代方法与路径条件化的协同作用，提出一系列方法论贡献，推动高斯过程在现代大规模场景中的应用。通过两者有机结合，昂贵的计算被表示为线性方程组的求解，并利用迭代线性求解器实现。这显著降低了内存需求，使模型可应用于更大规模数据；同时引入矩阵乘法作为主要运算，契合现代硬件特性。
原文摘要 · Abstract (English)
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for massively-parallel computation, prompting many researchers to develop techniques which improve their scalability. This dissertation focuses on the powerful combination of iterative methods and pathwise conditioning to develop methodological contributions which facilitate the use of Gaussian processes in modern large-scale settings. By combining these two techniques synergistically, expensive computations are expressed as solutions to systems of linear equations and obtained by leveraging iterative linear system solvers. This drastically reduces memory requirements, facilitating application to significantly larger amounts of data, and introduces matrix multiplication as the main computational operation, which is ideal for modern hardware.
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