用张量分析重新推导最小二乘与神经网络回归，更清晰地揭示算法本质。
Tensor-Based Foundations of Ordinary Least Squares and Neural Network Regression Models
- 基于张量分析和矩阵运算，重构模型数学基础。
- 推导出完整算法形式，包含简化版反向传播算法。
- 适合想深入理解模型原理的科研人员与研究生。
本文提出一种全新的数学方法，用于推导普通最小二乘法和神经网络回归模型，突破了当前机器学习文献中的传统路径。通过运用张量分析和基础矩阵计算，系统性地详细阐述并拓展了两类模型的理论基础，最终呈现三个算法，其中包括一个简化的神经网络反向传播算法，充分展示了这一新数学框架的优势。
原文摘要 · Abstract (English)
This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor Analysis and fundamental matrix computations, the theoretical foundations of both models are meticulously detailed and extended to their complete algorithmic forms. The study culminates in the presentation of three algorithms, including a streamlined version of the Backpropagation Algorithm for Neural Networks, illustrating the benefits of this new mathematical approach.
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