Term of Award
Spring 2024
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
Digital Commons@Georgia Southern License
Department
Department of Mathematical Sciences
Committee Chair
Dr. Divine Wanduku
Committee Member 1
Dr. Charles Champ
Committee Member 2
Dr. Shijun Zheng
Abstract
In this thesis, the Weighted Newton-Raphson Method (WNRM), an innovative optimization technique, is introduced in statistical supervised learning for categorization and applied to a diabetes predictive model, to find maximum likelihood estimates. The iterative optimization method solves nonlinear systems of equations with singular Jacobian matrices and is a modification of the ordinary Newton-Raphson algorithm. The quadratic convergence of the WNRM, and high efficiency for optimizing nonlinear likelihood functions, whenever singularity in the Jacobians occur allow for an easy inclusion to classical categorization and generalized linear models such as the Logistic Regression model in supervised learning. The WNRM is thoroughly investigated in the logistic regression model for both repeated and non-repeated response variables. Furthermore, the method is applied to obtain the best-fitted predictive logistic regression model for diabetes health status that depends on several predictor factors for the patients surveyed in a real-life study.
Recommended Citation
Debnath, Toma, "Classification in Supervised Statistical Learning With the New Weighted Newton-Raphson Method" (2024). Electronic Theses and Dissertations. 2725.
https://digitalcommons.georgiasouthern.edu/etd/2725
Research Data and Supplementary Material
No
