用Samplet方法将高斯过程计算复杂度从立方级降至对数线性，提升大规模数据处理效率。
Constructing Gaussian Processes via Samplets
- 基于Samplet构造高斯过程，通过优化参数实现最优收敛率
- 将传统立方复杂度降低至对数线性，支持高效训练与回归
- 适合需要快速建模且关注理论性能的低维数据研究者
高斯过程在大规模数据建模和模型选择方面面临主要挑战。本硕士论文聚焦低维情形，结合近期收敛结果，识别出具有最优收敛速率的模型及关键参数。基于该模型，提出一种基于Samplet的高效构建与训练方法，将原本立方级的计算复杂度降至对数线性级别。该方法在保持最优回归性能的同时显著提升计算效率，适用于大规模低维数据场景。
原文摘要 · Abstract (English)
Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to identify models with optimal convergence rates and pinpoint essential parameters. Utilizing this model, we propose a Samplet-based approach to efficiently construct and train the Gaussian Processes, reducing the cubic computational complexity to a log-linear scale. This method facilitates optimal regression while maintaining efficient performance.
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