Polynomial regression pipeline in ML Python - Model Pipeline Trace

Model Pipeline - Polynomial regression pipeline

This pipeline shows how polynomial regression learns to fit curved data by adding extra features that are powers of the original input. It transforms data, trains a model, and improves predictions over time.

Data Flow - 5 Stages

1Raw Data Input

1000 rows x 1 column→Collect original single feature data points→1000 rows x 1 column

x = [1, 2, 3, 4, 5]

↓

2Polynomial Feature Expansion

1000 rows x 1 column→Create new features by raising input to powers 1 and 2 (x and x^2)→1000 rows x 2 columns

x = [1, 2, 3], transformed to [[1, 1], [2, 4], [3, 9]]

↓

3Train/Test Split

1000 rows x 2 columns→Split data into 800 training rows and 200 testing rows→Train: 800 rows x 2 columns, Test: 200 rows x 2 columns

Train features shape: (800, 2), Test features shape: (200, 2)

↓

4Model Training

Train: 800 rows x 2 columns→Fit linear regression model on polynomial features→Trained model with 2 coefficients plus intercept

Model learns weights for x and x^2 terms

↓

5Model Evaluation

Test: 200 rows x 2 columns→Predict and compare to true values to compute loss and R^2 score→Loss scalar and R^2 score scalar

Loss = 0.15, R^2 = 0.92

Training Trace - Epoch by Epoch

Loss
1.0 |*       
0.8 | *      
0.6 |  *     
0.4 |   *    
0.2 |    *   
0.0 +--------
      1 2 3 4 5 Epochs

Epoch	Loss ↓	Accuracy ↑	Observation
1	0.85	0.45	Model starts with high loss and low accuracy
2	0.50	0.70	Loss decreases as model learns polynomial relationship
3	0.30	0.85	Model fits data better, accuracy improves
4	0.20	0.90	Loss continues to decrease, model converging
5	0.15	0.92	Final epoch shows good fit with low loss and high accuracy

Prediction Trace - 4 Layers

Layer 1: Input Feature

Layer 2: Polynomial Feature Expansion

Layer 3: Linear Model Prediction

Layer 4: Output Prediction

Model Quiz - 3 Questions

What does the polynomial feature expansion stage do?

A Calculates loss and accuracy

B Splits data into training and testing sets

C Adds new features by raising input to powers

D Predicts output values

Key Insight

Polynomial regression improves simple linear models by adding powers of input features, allowing the model to fit curved patterns in data. Training shows loss decreasing and accuracy increasing, confirming the model learns the relationship well.