1) General Idea
- Micro averaging aggregates the contributions of all classes before computing the metric.
- In other words:
- Add up True Positives (TP), False Positives (FP), and False Negatives (FN) across all classes.
- Then compute the metric once from these totals.
Every sample has equal weight, not every class.
2) Example with Precision
Suppose 3 classes (A, B, C):
- Class A: TP=90, FP=10
- Class B: TP=30, FP=20
- Class C: TP=5, FP=15
Macro Precision = (Prec_A + Prec_B + Prec_C)/3
= (90/100 + 30/50 + 5/20) / 3
= (0.90 + 0.60 + 0.25) / 3 = 0.583
Micro Precision = (TP_A + TP_B + TP_C) / (TP_A + TP_B + TP_C + FP_A + FP_B + FP_C)
= (90+30+5) / (90+30+5+10+20+15)
= 125 / 170 = 0.735
Notice:
- Macro treats each class equally (so class C’s bad score hurts a lot).
- Micro favors classes with more samples/events (so A dominates).
3) Micro Recall
Formula:
$\text{Micro Recall} = \frac{\sum_i TP_i}{\sum_i (TP_i + FN_i)}$
It’s the same as computing recall after pooling all classes.
In a single-label classification problem, micro precision = micro recall = accuracy.
4) Micro F1
- Since micro precision = micro recall in single-label classification,
→ Micro F1 = that same value. - In multi-label classification (where each sample can have multiple labels), micro F1 ≠ accuracy, but the same aggregation principle applies.
5) Micro AUROC
- Similar to macro:
- Collect all predictions and labels across classes.
- Compute AUROC once across the pooled dataset.
- Effectively, large classes dominate the AUROC score.
6) Quick Comparison Table
| Method | Weighting principle | Good for… |
|---|---|---|
| Macro | Equal weight per class | Checking fairness across classes (especially minority ones) |
| Micro | Equal weight per sample | Checking overall performance, dominated by majority classes |
| Weighted | Weight by class frequency | Middle ground: balances per-class fairness with sample size |
Summary:
- Micro averaging = count everything first, compute once → focuses on overall accuracy-like behavior.
- Macro averaging = compute per class, then average → focuses on balanced treatment of all classes.