Polynomial features in ML Python - Model Pipeline Trace

Model Pipeline - Polynomial features

This pipeline shows how polynomial features transform simple input data to help a model learn more complex patterns by adding powers and interaction terms.

Data Flow - 4 Stages

1Raw input data

1000 rows x 2 columns→Original features: two numeric columns→1000 rows x 2 columns

[[2, 3], [1, 4], [0, 5]]

↓

2Polynomial feature expansion

1000 rows x 2 columns→Add squared terms and interaction term (degree=2)→1000 rows x 5 columns

[[2, 3, 4, 6, 9], [1, 4, 1, 4, 16], [0, 5, 0, 0, 25]]

↓

3Model training

800 rows x 5 columns→Train model on training set (80% split)→Model trained on 800 rows x 5 columns

Model learns weights for each polynomial feature

↓

4Model evaluation

200 rows x 5 columns→Evaluate model on test set (20% split)→Performance metrics computed

Test loss and accuracy calculated

Training Trace - Epoch by Epoch

Loss
0.5 |****
0.4 |***
0.3 |**
0.2 |*
0.1 | 
     1 2 3 4 5 Epochs

Epoch	Loss ↓	Accuracy ↑	Observation
1	0.45	0.60	Model starts learning with high loss and moderate accuracy
2	0.30	0.75	Loss decreases and accuracy improves as model fits polynomial features
3	0.20	0.85	Model captures nonlinear patterns better
4	0.15	0.90	Loss continues to decrease, accuracy rises
5	0.12	0.92	Training converges with low loss and high accuracy

Prediction Trace - 3 Layers

Layer 1: Input sample

Layer 2: Polynomial feature expansion

Layer 3: Model prediction

Model Quiz - 3 Questions

What does polynomial feature expansion add to the original data?

A Random noise to increase data size

B New features with powers and interactions of original features

C Only the original features duplicated

D Labels for supervised learning

Key Insight

Polynomial features let a simple model learn more complex patterns by adding powers and interactions of original features, improving accuracy on nonlinear data.