对比两种线性回归求解方法的优劣，助你选对工具
Comparing the Moore-Penrose Pseudoinverse and Gradient Descent for Solving Linear Regression Problems: A Performance Analysis
- 用闭式解和迭代法分别求解线性回归问题
- 在合成与真实数据上验证了两者的耗时与稳定性差异
- 适合需要权衡精度与效率的机器学习实践者参考
本文对比了求解线性回归问题的两种基础方法：闭式解的Moore-Penrose伪逆与迭代式的梯度下降法。线性回归是预测建模的核心，求解器的选择显著影响效率与准确性。文章回顾并讨论了两种方法的理论基础，分析其计算复杂度，并在具有可控特性的合成数据集及经典真实数据集上评估其实证表现。结果明确了在计算时间、数值稳定性和预测精度方面，各方法各自的适用条件。本研究旨在为机器学习领域的研究人员与实践者在选择精确闭式解与近似迭代解时提供实用指导。
原文摘要 · Abstract (English)
This paper investigates the comparative performance of two fundamental approaches to solving linear regression problems: the closed-form Moore-Penrose pseudoinverse and the iterative gradient descent method. Linear regression is a cornerstone of predictive modeling, and the choice of solver can significantly impact efficiency and accuracy. I review and discuss the theoretical underpinnings of both methods, analyze their computational complexity, and evaluate their empirical behavior on synthetic datasets with controlled characteristics, as well as on established real-world datasets. My results delineate the conditions under which each method excels in terms of computational time, numerical stability, and predictive accuracy. This work aims to provide practical guidance for researchers and practitioners in machine learning when selecting between direct, exact solutions and iterative, approximate solutions for linear regression tasks.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。