What is weighted averaging in multiclass evaluation?

What is weighted averaging in multiclass evaluation?

Weighted averaging summarizes a multiclass precision, recall, or F1-score by giving each class a weight proportional to its support—the number of true examples belonging to that class.

How is it calculated?

1. Find each class's precision, recall, or F1-score.
2. Count its support (actual examples of that class).
3. Multiply its metric by its support, add across classes, and divide by the total support.

Weighted metric = Σ(class metric × class support) / Σ(class support).

Beginner-friendly numerical example

A classifier predicts the labels Cat, Dog, and Bird for 100 photographs:

• Cat: support 70, F1 = 0.90
• Dog: support 20, F1 = 0.70
• Bird: support 10, F1 = 0.40

Weighted F1 = (70 × 0.90 + 20 × 0.70 + 10 × 0.40) / 100 = (63 + 14 + 4) / 100 = 0.81.

This illustrates the weighting arithmetic with illustrative per-class scores. In practice, compute the scores from predictions, then weight them by observed class support.

Why use it?

• It reflects the dataset's actual class distribution.
• It provides one summary when common categories contribute more examples.
• It can be useful for monitoring overall model performance on imbalanced datasets.

Important limitations

• A high weighted score can hide weak performance on a rare but important class—here Bird's F1 is only 0.40.
• Weighted recall equals accuracy in ordinary single-label multiclass classification when all labels are included; weighted precision and weighted F1 do not generally equal accuracy.
• Weighted F1 is not necessarily the harmonic mean of weighted precision and weighted recall, because each class's F1 is computed first and then averaged.
• If classes have different *business costs*, class support alone does not capture those costs. Check per-class results and consider cost-sensitive evaluation.

Python example

PYTHON
from sklearn.metrics import precision_recall_fscore_support

precision, recall, f1, support = precision_recall_fscore_support(
    y_true, y_pred, average="weighted", zero_division=0
)
print(f"Weighted F1: {f1:.3f}")

With average="weighted", the returned support value is None; per-class support is available with average=None.

Remember: Weighted averaging answers, “How well does the model perform when classes contribute in proportion to how frequently they appear in the test set?”

Reference: scikit-learn precision_recall_fscore_support.