Categorical and geometric methods in statistical, manifold, and machine learning

TL;DR

This paper explores categorical and geometric techniques applied to statistical, manifold, and machine learning problems, emphasizing probabilistic morphisms and their applications across various learning contexts.

Contribution

It introduces and discusses the use of probabilistic morphisms and geometric methods in solving problems in statistical, manifold, and machine learning, expanding theoretical frameworks.

Findings

Probabilistic morphisms provide a unifying framework for diverse learning problems.

Geometric methods enhance understanding of manifold learning techniques.

Applications demonstrate the versatility of categorical approaches in machine learning.

Abstract

We present and discuss applications of the category of probabilistic morphisms, initially developed in \cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics, considered in depth in the forthcoming book \cite{LMPT2024}.