The EM Algorithm in Information Geometry

Abstract

The purpose of this thesis is to convey the basic concepts of information geometry and its applications to non-specialists and those in applied fields, assuming only a first-year undergraduate background in calculus, linear algebra, and probability theory / statistics. We first begin with an introduction to the EM algorithm, providing a typical use case in Python, before moving to an overview of basic Riemannian geometry. We then introduce the core concepts of information geometry and the $em$ algorithm, with an explicit calculation of both the $e$ and $m$ projection, before closing with a discussion of an important application of this research to the field of deep learning, providing a novel implementation in Python.