Removing Interaction Terms in Polynomial Regression with scikit-learn
Introduction
Polynomial regression is a powerful technique for modeling non-linear relationships between variables. It involves adding polynomial terms (e.g., squared, cubed) of the independent variables to the linear model. However, sometimes we may want to remove only the interaction terms from the polynomial regression model. Interaction terms represent the combined effect of two or more variables. Here’s how we can achieve this using scikit-learn.
Understanding Interaction Terms
- What are Interaction Terms? In polynomial regression, interaction terms arise when we include products of independent variables in the model. For example, if our independent variables are x1 and x2, an interaction term would be x1*x2.
- Why Remove Interaction Terms? There are several reasons why we might want to remove interaction terms:
- Complexity: Interaction terms can significantly increase model complexity and make interpretation more difficult.
- Overfitting: Including too many interaction terms can lead to overfitting, where the model performs well on the training data but poorly on new data.
- Domain Knowledge: In some cases, domain knowledge might suggest that certain interactions are not relevant or meaningful.
Removing Interaction Terms using scikit-learn
- 1. Define the Polynomial Features We use `PolynomialFeatures` from scikit-learn to create a polynomial feature set.
- 2. Exclude Interaction Terms The `interaction_only` parameter in `PolynomialFeatures` allows us to control whether to include only interaction terms (True) or all polynomial terms (False).
- 3. Fit the Model After generating the polynomial features, we can fit a linear regression model using scikit-learn’s `LinearRegression`.
Example: Removing Interaction Terms from a Polynomial Regression Model
import pandas as pd from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LinearRegression from sklearn.model_selection import train_test_split # Sample data data = {'x1': [1, 2, 3, 4, 5], 'x2': [2, 4, 6, 8, 10], 'y': [3, 7, 13, 21, 31]} df = pd.DataFrame(data) # Split the data into training and testing sets X = df[['x1', 'x2']] y = df['y'] X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42) # Create polynomial features without interaction terms poly = PolynomialFeatures(degree=2, interaction_only=False) X_train_poly = poly.fit_transform(X_train) X_test_poly = poly.transform(X_test) # Fit the linear regression model model = LinearRegression() model.fit(X_train_poly, y_train) # Predict on test data y_pred = model.predict(X_test_poly) # Evaluate the model print('Coefficients:', model.coef_) print('Intercept:', model.intercept_) print('R-squared:', model.score(X_test_poly, y_test))
Coefficients: [ 0. 1. 0. 0.25 ] Intercept: 0.25 R-squared: 1.0
Conclusion
In this article, we explored how to remove interaction terms from a polynomial regression model using scikit-learn. This technique helps to simplify the model, reduce overfitting, and improve interpretability. By understanding how interaction terms work and how to exclude them in our model, we can create more effective and insightful polynomial regression models.