Feature Engineering Studio
Keep the learner fixed and change only φ(x): raw x, standardized x, x², or bucket indicators—then inspect the design row and prediction terms.
A representation-first regression lab. The same train/validation split and ordinary least-squares learner are refitted after each feature transformation so students can separate a model's learning rule from the information made available in its feature vector.
Step by step
- Start from raw x and fit an ordinary straight-line model on the training split.
- Standardize x using mean and standard deviation calculated only from training x.
- Add x² to the feature vector so the same linear learner can represent curvature.
- Replace exact x with fixed range indicators to see what bucketing preserves and discards.
- Inspect the selected sample's design vector φ(x), fitted coefficients β, and each βⱼφⱼ contribution.
- Compare train and held-out validation MSE/R² while changing only the representation.
Core formulas
Feature map
x → φ(x)Feature engineering changes the representation consumed by the learner.
Linear prediction
ŷ = βᵀφ(x)The learner stays linear in fitted coefficients even when φ includes nonlinear raw-data transforms.
Training-only standardization
z = (x − μ_train) / σ_trainTransformation statistics are learned from training data and then reused on validation data.
When to use Feature Engineering Studio
- Understanding the difference between model capacity and input representation.
- Seeing why polynomial features can expose curvature to a linear learner.
- Learning what normalization and bucketing do to the actual feature vector.