A Viewpoint of Algebraic Geometry in Singular Learning Theory

Abstract

In this thesis, the goal of singular learning theory and its methods are described. To resolve the singularity problem, we will introduce resolution of singularities, the notion in algebraic geometry. In addition, we will go over some examples of singular learning theory (focus on strictly singular model) and show how to resolve singularities by computation. In particular, in the reduced rank regression model, the process of resolution will be described by taking blow-ups. Finally, we will introduce a determinantal variety, and examine the possibility of connection with the reduced rank regression model.