Optimization Techniques in Machine Learning: Mathematical Models and Applications
Abstract
This research investigates the role of mathematical optimization techniques—genetic algorithms (GAs), stochastic optimization, and gradient descent programming—in enhancing the performance of machine learning (ML) models and the study aims to bridge theoretical frameworks with practical implementations by analyzing the mathematical foundations of these methods and their applications in data analysis and complex model prediction and through rigorous evaluation, the results demonstrate that GAs excel in non-convex optimization tasks, achieving 15% higher clustering accuracy than traditional methods, while adaptive gradient descent variants like Adam reduce training time by 30% in deep neural networks. Stochastic optimization techniques, particularly variance-reduced SGD, significantly improve convergence rates in large-scale learning tasks and these findings underscore the transformative potential of optimization-driven ML in addressing real-world challenges, from healthcare diagnostics to financial forecasting.
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