Macro Precision

1. Precision Recap (Binary Case)

• Precision = Of all items the model predicted as positive, how many were actually positive?

$Precision = \frac{TP}{TP + FP}$

Where:

• TP = True Positives
• FP = False Positives

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2. Precision in Multiclass Problems

When you have K classes, each class can be considered in a one-vs-rest (OvR) fashion:

• Compute precision for each class individually (as if that class = “positive” and all others = “negative”).

Example (3 classes: A, B, C):

• Precision(A) = TP_A / (TP_A + FP_A)
• Precision(B) = TP_B / (TP_B + FP_B)
• Precision(C) = TP_C / (TP_C + FP_C)

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3. Macro Precision Definition

• Take the arithmetic mean of precision values across all classes.

$Precision_{macro} = \frac{1}{K} \sum_{i=1}^{K} Precision_i$

• Each class contributes equally, regardless of how many samples that class has.

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4. Macro vs Micro vs Weighted

• Macro Precision: Average across classes equally. Good when you want fairness across classes.
• Micro Precision: Compute global TP and FP across all classes, then calculate precision. More influenced by large classes.
• Weighted Precision: Average precision per class but weighted by the number of samples in each class.

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5. Example

Suppose a 3-class classifier:

• Precision(A) = 0.80
• Precision(B) = 0.60
• Precision(C) = 0.40
• Macro Precision = (0.80 + 0.60 + 0.40) / 3 = 0.60
• If class C is very small, Macro Precision still penalizes the model because each class counts equally.

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Summary

• Macro Precision = average precision across all classes (equal weight per class).
• Useful when all classes are equally important, even if some are rare.
• Different from Micro Precision, which weights by sample counts.