Ridge regression hyperparameter sweep (log-spaced $\lambda$) on the scikit-learn Diabetes dataset, with optional quadratic polynomial features (pairwise products + original features), including saved MSE-vs-λ plots and a patient-style prediction example.

• Loads the Diabetes regression dataset from scikit-learn
• Splits data by order: first 90% train, last 10% validation
• Trains and evaluates:
  • Linear regression (closed-form) on original features
  • Linear regression (closed-form) on polynomial features (degree-2 cross terms + originals)
  • Ridge regression (closed-form) over a sweep of 50 $\lambda$ values on both feature sets
• Saves two plots:
  • outputs/figures/ridge_mse_original_features.png
  • outputs/figures/ridge_mse_poly_features.png
• Selects the best ridge model by lowest validation MSE
• Uses the best polynomial ridge model to predict disease progression for a provided patient profile (Exercise 3.9 style)

GitHub Markdown doesn’t reliably support image resizing via ![](...), so these are embedded with HTML and a fixed width.

python -m venv .venv
# macOS/Linux
source .venv/bin/activate
# Windows (PowerShell)
.\.venv\Scripts\Activate.ps1

pip install -r requirements.txt

python scripts/run_all.py

This will:

• print train/validation MSEs for linear and ridge models
• save the two plot images into outputs/figures/
• write a metrics summary JSON to outputs/metrics/run_summary.json

python scripts/predict_patient.py

After running scripts/run_all.py, you should see:

• outputs/figures/ridge_mse_original_features.png
• outputs/figures/ridge_mse_poly_features.png
• outputs/metrics/run_summary.json (created/overwritten each run)

• Closed-form solutions:
  • Linear regression uses a pseudo-inverse for stability.
  • Ridge regression uses np.linalg.solve on the normal equations with ridge penalty.
• Intercept regularization:
  • By default, the intercept term is not regularized (regularize_intercept=False), which is the common ridge convention.
• Polynomial features:
  • The feature map includes all pairwise products $x_i x_j$ for $i<j$, and then appends the original features.
• Scaling for the patient example:
  • The provided patient vector is in the original feature scale.
  • The script reproduces the scaling used by sklearn.datasets.load_diabetes(scaled=True) with this feature-wise transform:

• Scaling parameters are computed from load_diabetes(scaled=False).

This project uses the Diabetes dataset shipped with scikit-learn:

• https://scikit-learn.org/stable/datasets/toy_dataset.html#diabetes-dataset

MIT (see LICENSE).