Minimum Gamma Divergence for Regression and Classification Problems

Abstract: The book is structured into four main chapters. Chapter 1 introduces the foundational concepts of divergence measures, including the well-known Kullback-Leibler divergence and its limitations. It then presents a detailed exploration of power divergences, such as the $\alpha$, $\beta$, and $\gamma$-divergences, highlighting their unique properties and advantages. Chapter 2 explores minimum divergence methods for regression models, demonstrating how these methods can improve robustness and efficiency in statistical estimation. Chapter 3 extends these methods to Poisson point processes, with a focus on ecological applications, providing a robust framework for modeling species distributions and other spatial phenomena. Finally, Chapter 4 explores the use of divergence measures in machine learning, including applications in Boltzmann machines, AdaBoost, and active learning. The chapter emphasizes the practical benefits of these measures in enhancing model robustness and performance.