Polynomial expansion transforms input features by adding powers and products of features up to a specified degree.
Polynomial basis expansion extends input data with feature powers and systematic interactions up to a chosen degree. Interactions help regression capture feature synergy, while powers let a linear model represent curves. section 4.3.2
Use the technique with care:
Choose a degree with PolynomialFeatures; degree 2 can create squared terms and pairwise products. section 4.3.2
Expect many more features, along with greater noise, multicollinearity, and overfitting risk. section 4.3.2
Combine the expansion with Ridge to shrink coefficients or Lasso to select a smaller set of terms. section 4.3.2
How Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI covers it
How deep it goes
Defines generated powers and interactions, demonstrates degree selection and regularization, but does not derive feature-count formulas.
Examples
Uses the expansion a² + 2ab + b² and a degree-two Scikit-learn pipeline evaluated with cross-validation.
What you can do after
Apply it via Scikit-learn and control its complexity with Ridge or Lasso regularization.
How it connects
Connects polynomial features with linear regression, Ridge regression, Lasso regression, multicollinearity, and overfitting.
This explainer was generated by Manning's knowledge graph from the text of Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI. The section links point to the parts of the book it draws on.
