Feature Engineering: Keep the Coordinates Stable

• A fitted transform includes parameters and column order.
• Split first; fit on training rows; reuse on held-out rows.
• Repeat fitting within each cross-validation training fold.

Min-max worked example

Train: [[2,10,7],[4,20,7],[6,30,7]]

• Save mins=[2,10,7], maxs=[6,30,7].
• Training outputs: [[0,0,0],[0.5,0.5,0],[1,1,0]].
• Course zero-span policy: output zero.

Held-out values can leave the range

New row [8,15,9] transforms to [1.5,0.25,0].

• Reuse training minima/maxima; do not refit.
• No clipping is required.
• Zero-span columns always return zero in this exercise.

Standardization stores an effective scale

Train: [[1,7],[3,7]]

• Means [2,7]; population variances [1,0] using /n.
• Saved stds=[1,1]; constant columns use scale one.
• Training outputs [[-1,0],[1,0]]; held-out [5,9] -> [3,2].
• Standardization does not make a distribution normal.

One-hot positions carry meaning

Saved categories: ["bird","cat","dog"]

• cat -> [0,1,0]
• bird -> [1,0,0]
• dog -> [0,0,1]
• Reuse this order even if a prediction batch omits a category.

Unknown categories

• fox -> [0,0,0] under the exercise policy.
• decode([0,0,0],categories) -> None.
• Width stays fixed; unknown identity is lost.
• Exactly one 1 applies only to known values.

Scaling is a modeling choice

• It changes distance contributions and coefficient penalties.
• Outliers influence ranges, means, and variances.
• A count, flag, and ordinal feature may need different treatment.
• Validate the representation using held-out performance.

Extend with the same fit boundary

• Imputation statistics and selected features come from training data.
• Interactions can expose nonlinear structure.
• Target encoding needs out-of-fold training features.
• Save preprocessing state with the trained model.