Investigation Of Information Geometry For Machine Learning And Statistical Inference Applications

Abstract

A mathematical framework called information geometry offers a potent set of tools for deciphering and comprehending the geometrical structure of probability distributions. Information geometry has attracted increasing attention in recent years for applications in machine learning and statistical inference. Through the use of information geometry's distinctive geometric perspective, this study seeks to investigate how these disciplines could be improved. The basic ideas of information geometry, such as the Fisher information metric and the Riemannian manifold of probability distributions, are first introduced in the investigation. It then explores the numerous applications of information geometry to statistical inference and machine learning. A foundation for comprehending the geometry of optimisation landscapes in machine learning is also provided by information geometry. We
can learn more about the convergence behaviour of optimisation algorithms by examining the curvature and geometric characteristics of the objective function, which will help us develop better training methods and more effective learning algorithms. Additionally,
information geometry presents a fresh viewpoint on statistical inference issues. As a result, we are able to investigate the geometrical properties of statistical models and create effective estimating methods that take advantage of the inherent geometry of the parameter space. This results in more accurate estimations and trustworthy inference techniques.