Analysis of Information Geometry for Optimization and Inference Applications

Abstract

A mathematical framework called "information geometry" investigates the geometrical attributes and features of probability distributions and statistical models. In a variety of domains, including as machine learning, optimisation, and inference, it offers a potent toolkit for analysing and optimising complicated systems. Information geometry and its uses in optimisation and inference are examined in this work.First, we give a general overview of information geometry's foundational ideas and principles, including topics like the Fisher information metre, divergence measures, and exponential families. We go over how to quantify the geometric links between probability distributions and derive practical geometric structures using these ideas.The use of information geometry in optimisation issues is what we investigate next. We show how the Fisher information metric can direct effective search strategies and convergence analysis in optimisation algorithms by utilising its geometric characteristics. We go over the benefits of applying information geometry to a variety of optimisation tasks, including parameter estimation, model choice, and neural network training. We also look into how information geometry affects statistical inference. We emphasise how the development of effective and reliable inference algorithms is made possible by the geometric structures of exponential families. We go over the use of divergence measures to quantify the differences between distributions, making tasks like model comparison and hypothesis testing easier.We also review current developments in information geometry, especially its application to probabilistic programming and deep learning. We go over how information geometry can improve deep neural networks' capacity for generalisation, interpretation, and uncertainty estimation.In this study, information geometry and its uses in optimisation and inference are thoroughly studied. Information geometry provides useful insights and methods for resolving challenging issues in a variety of fields by taking advantage of the geometric aspects of probability distributions.