Hands-on Experience with Gaussian Processes (GPs): Implementing GPs in Python - I

TL;DR

This paper provides a practical guide for implementing Gaussian Processes in Python from scratch, focusing on understanding the underlying mechanics and inference methods without relying on external libraries.

Contribution

It offers an educational approach to building GPs in Python using minimal dependencies, enhancing understanding of the core concepts and inference techniques.

Findings

Developed a Python-based GP implementation from scratch

Demonstrated GP inference using maximum likelihood estimation

Provided examples with 1D spatial data

Abstract

This document serves to complement our website which was developed with the aim of exposing the students to Gaussian Processes (GPs). GPs are non-parametric Bayesian regression models that are largely used by statisticians and geospatial data scientists for modeling spatial data. Several open source libraries spanning from Matlab [1], Python [2], R [3] etc., are already available for simple plug-and-use. The objective of this handout and in turn the website was to allow the users to develop stand-alone GPs in Python by relying on minimal external dependencies. To this end, we only use the default python modules and assist the users in developing their own GPs from scratch giving them an in-depth knowledge of what goes on under the hood. The module covers GP inference using maximum likelihood estimation (MLE) and gives examples of 1D (dummy) spatial data.