Week 11 Summary: Uncertainty-aware regression & Gaussian Processes

Cross-Book Summary

1. Knowing what you don’t know

• Aleatoric vs. Epistemic: Inherent physical noise vs. model ignorance.
• Overconfidence Danger: Point estimates fail safely in unknown regimes; uncertainty metrics are crucial.

2. Gaussian Processes (GPs)

• Distribution over Functions: GP yields posterior mean and variance (uncertainty).
• Kernels as Physical Priors: Encodes assumptions about data smoothness/scale.
• Non-Parametric Nature: Scales with data size, ideal for small, high-quality materials datasets.

3. GP-Based Process Maps

• Confidence Ribbons: Visualize reliability to guide further experiments.
• Kriging: Interpolates materials property surfaces using GP regression.

90-Minute Lecture Strategy

Part 1: Uncertainty in Science

• Risk management in materials processing.
• Visualizing distributions and error bars.

Part 2: GP Fundamentals

• Function vs. Parameter space.
• Kernels and “Similarity”.
• Conditional Gaussians and Variance.

Part 3: GP Case Studies

• Predicting tensile strength across parameters.
• GP for Experimental Design.
• Multi-Task GPs.

Part 4: Advanced Probabilistic ML

• Mixture Density Networks (MDNs).
• Dropout as Bayesian approximation.

Part 5: Decision Making

• Safe process windows via confidence intervals.
• Building trustworthy models.

Quarto Website Update (Summary)

Summary for ML-PC Week 12:
- Introduces Probabilistic Machine Learning for uncertainty quantification. - Differentiates aleatoric (noise) from epistemic (ignorance) uncertainty. - Uses Gaussian Processes (GPs) for uncertainty-aware regression. - Applies confidence intervals to map robust process windows.