Gaussian Processes, Bayesian Optimization, and gpCAM
by Marcus M. Noack and Maher Alghalayini

Table of Contents

Introduction to Machine Learning

• Taxonomy of ML approaches: supervised, unsupervised, active, probabilistic.

• Function Learning vs Learning Geometry.

• Some example methodologies and where they fit in.

• GPs and why probabilistic ML matters for science: decisions under uncertainty.

Gaussian Processes in a Nutshell

• What is a GP? The function-space view (priors over functions, not parameters).

• The kernel as the scientific assumption: smoothness, periodicity, scale.

• Prior → posterior: how observations update the GP.

• Mean prediction + uncertainty quantification — why both matter.

• Honest UQ: what calibration means and why it's non-trivial.

• Live interactive visualization: prior samples, kernel choices, posterior updating.

• Hands-on: modify a kernel in a pre-built Colab; observe how the posterior changes.

Building a GP Model with gpCAM (In Colab)

• Input space, output space, kernel selection.

• Prior mean and noise.

• Training.

• Posterior evaluations and performance metrics.

Bayesian Optimization with gpCAM (In Colab)

• BO vs GPs.

• Creating a full optimization loop.

• Acquisition Functions.

• Asking for new suggestions.

gpCAM AI Agent Integration

• Setting up the agent in Claude Code and Colab.

• Using the agent.

• Group Challenge.