Roberto Dias Algarte

Roberto Dias Algarte

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.

Roberto Dias Algarte

This article presents a generic approach to convolution that significantly differs from conventional methodologies in the current Machine Learning literature. The approach, in its mathematical aspects, proved to be clear and concise, particularly when high-order tensors are involved. In this context, a rational theory of regression in neural networks is developed, as a framework for a generic view of sparse convolutional neural networks, the primary focus of this study. As a direct outcome, the classic Backpropagation Algorithm is redefined to align with this rational tensor-based approach and presented in its simplest, most generic form.