Tensor-Based Foundations of Ordinary Least Squares and Neural Network Regression Models

• URL: http://arxiv.org/abs/2411.12873v1
• Date: Tue, 19 Nov 2024 21:36:04 GMT
• Title: Tensor-Based Foundations of Ordinary Least Squares and Neural Network Regression Models
• Authors: Roberto Dias Algarte,
• Abstract summary: This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models. By leveraging Analysis and fundamental matrix computations, the theoretical foundations of both models are meticulously detailed and extended to their complete algorithmic forms.
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• Abstract: 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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