Tutorial: Laplace Hessian Comparison¶

Notebook: Laplace_HessianComparison_Tutorial.ipynb

Purpose¶

Compare all Laplace Hessian structures on one shared MAP model and dataset.

Data Setup¶

• Nonlinear 1D regression
• Train/validation/test split in the same support
• OOD plotting range outside train support

Core Logic¶

• Train one MAP MLP checkpoint
• Fit each structure with LaplaceWrapper
• Tune prior precision by validation NLL
• Compare metrics and uncertainty profiles

Metrics¶

• RMSE / MAE / NLL
• 95% coverage and interval width
• ID vs OOD predictive standard deviation ratio

Scientific Details¶

• Equations, derivations, and references for all six Hessian structures:
• Laplace method scientific reference

Related Notebooks¶

• Laplace_Tutorial.ipynb
• Laplace_FullHessian_Tutorial.ipynb