Stacking with out-of-fold predictions

Learn how much to trust each model

Stacking trains several base models, then learns how to combine their predictions. The meta-learner must see predictions on data the base models did not train on, otherwise it learns to trust whichever model overfit the most.

Implement two functions.

oof_predictions(model_fn, X, y, n_splits=3) returns an array of length n with out-of-fold predictions. Split the rows into n_splits contiguous blocks with no shuffling. For each block, call model_fn(X_train, y_train, X_block) on the other blocks, and store the result at the block's positions.

stacking_weights(P, y) takes P of shape (n, m), where each column is one base model's out-of-fold predictions, and returns the least-squares weights w of length m with no intercept, so that P @ w best matches y.

Constraints

• 2 ≤ n_splits ≤ n, otherwise raise ValueError.
• P must have as many rows as y, otherwise raise ValueError.
• Do not modify the inputs.

Hints