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Week 12 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.