NumPy Multiple Linear Regression GD

Build a from-scratch multiple linear regression trainer in pure NumPy: standardize features, minimize MSE with batch gradient descent and early stopping, compare against the normal equation, and report MAE, RMSE, and R-squared via a reusable model API.

How to run

python scaffold.py

Steps

• 1. shuffle_xy
• 2. split_train_val_test
• 3. compute_feature_stats
• 4. standardize_features
• 5. add_bias_column
• 6. prepare_design_matrix
• 7. predict_linear
• 8. mse_loss
• 9. mse_gradient
• 10. normal_equation
• 11. initialize_weights
• 12. gd_step
• 13. epoch_train_val_losses
• 14. update_early_stop_state
• 15. init_training_state
• 16. run_one_epoch
• 17. train_batch_gd
• 18. mean_absolute_error
• 19. root_mean_squared_error
• 20. r_squared
• 21. evaluate_regression
• 22. learning_curve_data
• 23. weights_l2_distance
• 24. create_lr_model
• 25. fit_lr_model
• 26. predict_lr_model
• 27. score_lr_model
• 28. compare_with_normal_equation

Results

Splits: 90 30 30
Sample preds: [-4.9349 -2.1614 -1.1088 -3.5913  1.7047]
Sample trues: [-4.8688 -2.2391 -0.8235 -3.5582  1.6763]
Test MAE/RMSE/R2: {'mae': 0.09220147681923264, 'rmse': 0.12202512653831676, 'r2': 0.9985479787094949}
GD vs normal-eq L2 gap: 0.005860423059766929
Final train/val MSE: 0.010137750731524809 0.012253596422242757
Epochs run: 81