Mathematical Foundations for Machine Learning (#1379)

Authors

Quiroz-Chavil, Helga Kelly

Capuñay-Uceda, Carlos Enrique

Collantes Santisteban, Luis Jaime

Collantes Santisteban, Samuel

Collantes Santisteban, Carlos Alberto

Collantes Alvarado, Kelly Scarlett

Abstract

This paper has conducted a comprehensive review of more than 30 machine learning (ML) and deep learning (DL) algorithms across four main categories: supervised, unsupervised, reinforcement and deep learning. The discussion focused on the description of each algorithm, the application of mathematical foundations in their implementation, and their relevance to various practical applications. Through this analysis, the critical importance of underlying mathematical and statistical concepts, such as optimization, probability theory, and geometry, in the development of ML and DL models was highlighted A key conclusion of the paper is the diversity and adaptability of ML and DL algorithms in a wide range of fields, including computer vision, natural language processing, robotics, and medicine. This analysis underscores how rapidly the field is advancing, marked by the evolution of complex models that have transformed machine learning and adaptive capabilities.However, the work also recognizes the challenges and limitations that exist in the design and implementation of these algorithms, including overfitting, interpretability, and computational consumption. These challenges underscore the need for continued research and development to optimize and create new techniques that overcome these barriers. Looking to the future, the work suggests a focus on developing even more generative models.