Stretch: bagging concept

The problem, from first principles

Majority voting needs trees that are not exact copies. Bagging creates that diversity by training the same learner on many same-sized random samples drawn with replacement. A row may appear repeatedly or not at all, but its label must always travel with it.

From theory to code

Implement bootstrap_sample and train_random_forest. Draw paired bootstrap rows, then train exactly n_trees with the existing build_tree function.

Constraints

• Bootstrap input and label arrays preserve their original shapes.
• Draw exactly input.shape[0] indices from [0, n_samples) with replacement.
• Use the same index array for input and labels.
• Build one np.random.default_rng(seed) before the tree loop.
• Return exactly n_trees independently bootstrapped build_tree results.
• Equal fixed seeds reproduce a call; a reused generator must advance between trees.

Hints

Open one at a time. Each gives away a little more than the last.