Sammy Suliman | Searcharxiv

arXiv2024

Lovasz' Conjecture and Other Applications of Topological Methods in Discrete Mathematics

In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as combinatorics, graph theory, and theoretical computer science. In this paper, we seek to provide an introduction to the relevant topological concepts to non-specialists, as well as a selection of some existing applications to theorems in discrete mathematics.

math.HO↗

arXiv2024

The EM Algorithm in Information Geometry

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.

math.HO↗