Macro-Average Precision and Recall, Macro-Average F-score:

In the context of multiclass classification, macro-average precision, macro-average recall, and macro-average F-score are metrics used to assess a model's performance by calculating precision, recall, and F-score separately for each class and then averaging them. Unlike micro-average metrics, macro-average metrics treat each class equally, without considering the size of the classes.


Macro-Average Precision:

·        Definition:

Ø  Macro-average precision calculates the precision for each class separately and then takes the average. It treats all classes equally.

·        Formula:

Macro-Average Precision = (Precision_Class1 + Precision_Class2 + ... + Precision_ClassN) / Number of Classes


Macro-Average Recall:

·        Definition:

Ø  Macro-average recall calculates the recall for each class individually and then takes the average. It treats each class equally in the overall recall computation.

·        Formula:

Macro-Average Recall = (Recall_Class1 + Recall_Class2 + ... + Recall_ClassN) / Number of Classes

 

Macro-Average F-score:

·        Definition:

Ø  Macro-average F-score is the harmonic mean of macro-average precision and macro-average recall.It provides a balanced measure across all classes without giving more importance to larger classes.

·        Formula:

Macro-Average F-score = (2 * Macro-Average Precision * Macro-Average Recall) / (Macro-Average Precision + Macro-Average Recall)

Example:

Suppose we have a multiclass classification model with three classes: "A," "B," and "C." After evaluation, we have the following results for precision and recall:

  • Precision for Class A: 0.8
  • Precision for Class B: 0.7
  • Precision for Class C: 0.9
  • Recall for Class A: 0.85
  • Recall for Class B: 0.75
  • Recall for Class C: 0.88

 

Now, we can calculate macro-average precision, macro-average recall, and macro-average F-score:

Macro-Average Precision = (0.8 + 0.7 + 0.9) / 3 = 2.4 / 3 = 0.8

Macro-Average Recall = (0.85 + 0.75 + 0.88) / 3 = 2.48 / 3 ≈ 0.827

Macro-Average F-score = (2 * 0.8 * 0.827) / (0.8 + 0.827) ≈ 1.655 / 1.627 ≈ 1.016