Class Imbalance

The problem, from first principles

01-stratified-sampling keeps the class mix when sampling an imbalanced dataset. Keeping the mix does not make the imbalance go away, and the imbalance is the problem. In fraud detection or disease screening, 99% of rows are one class, so a model that always predicts the majority class scores 99% accuracy and finds nothing. The standard remedies change what the model sees: weight the rare class more heavily in the loss, copy rare rows until the classes balance, throw away common rows, or invent new rare rows that lie between existing ones. This question builds all four.

From theory to code

Implement class_weights(y), which gives each class a loss weight inversely proportional to its frequency, then random_oversample(X, y, rng), which duplicates minority rows, then random_undersample(X, y, rng), which drops majority rows, then interpolate_minority(minority, n_new, rng), which creates synthetic minority points between real ones. The signatures and docstrings are already in the editor.

Constraints

• X is a 2D float array (rows, features) and y is a 1D array of class labels with one entry per row. rng is a numpy.random.Generator.
• class_weights returns a dict mapping each label to n_samples / (n_classes * count_of_that_class). The weights of the classes, multiplied by their counts, all sum to the same total, so every class carries equal total weight.
• random_oversample returns new (X_resampled, y_resampled) arrays that keep every original row first, in order, then append extra rows for each class below the largest class count. For each such class in sorted label order, draw needed = max_count - count row indices with rng.choice(rows_of_that_class, size=needed, replace=True) and append those rows. Every class ends with max_count rows.
• random_undersample returns new (X_resampled, y_resampled) where every class is cut to the smallest class count. For each class in sorted label order, keep rng.choice(rows_of_that_class, size=min_count, replace=False) indices. The result lists the kept rows class by class in sorted label order, each class's rows sorted by original index.
• interpolate_minority takes a 2D array of minority-class points and returns an array of shape (n_new, features). For each new point, in order, draw two distinct points a and b with rng.choice(len(minority), size=2, replace=False) and a weight u = rng.random() and return a + u * (b - a). It needs at least 2 minority points.
• Inputs must not be modified.

Hints