College of Graduate Studies: Theses & Dissertations

Term of Award

Spring 2026

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Divine Wanduku

Committee Member 1

Scott Kersey

Committee Member 2

Jiehua Zhu

Committee Member 3

Chidozie Chukwu

Abstract

Multiclass classification is a central problem in statistical learning, where model estimation relies on likelihood-based optimization in nonlinear settings. Within this framework, multinomial logistic regression provides a fundamental and interpretable approach for modeling class probabilities. Maximum likelihood estimation depends on iterative second-order optimization methods whose performance is highly sensitive to the conditioning of the curvature matrices. In practice, near-singularity, rank deficiency, or flat likelihood surfaces can lead to unstable updates, slow convergence, or failure. This study examines the Ordinary Newton--Raphson, Modified Newton--Raphson, Gauss--Newton, and Levenberg--Marquardt methods for multinomial logistic regression, with emphasis on ill-conditioned regimes where classical updates may diverge. Stabilized approaches using damping and curvature regularization improve numerical robustness while maintaining convergence. Model performance is evaluated using likelihood-based criteria (Akaike Information Criterion), and convergence behavior is examined through profile plots and curvature diagnostics. Simulation results show improved computational reliability in ill-conditioned classification problems, highlighting the importance of stabilized second-order optimization in statistical learning.

Research Data and Supplementary Material

No

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Available for download on Wednesday, April 16, 2031

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