Micro AUC

1) What it is

• Micro AUC = the ROC-AUC (or PR-AUC) computed after pooling all predictions and labels across classes.
• Instead of calculating per-class AUC, you flatten the multilabel/multiclass problem into one big binary problem:
  • Each prediction = “this instance belongs to class i” vs “it doesn’t.”
  • Pool all such decisions across all classes.

Micro AUC measures how well the model ranks all positive examples across all classes above all negative ones.

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2) Formula (conceptual)

Given $K$ classes, for each class $i$:

• Collect predictions $p_{i}$​ and true labels $y_{i}$​.
• Concatenate across all classes.
• Compute ROC-AUC (or PR-AUC) on this flattened dataset.

So, instead of averaging per-class AUCs, you treat everything as one large binary classification problem.

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3) Intuition

• Micro AUC gives a global probability ranking quality.
• Dominated by frequent classes, since each sample contributes equally.
• Contrast with Macro AUC: which treats each class equally.

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4) Example

Suppose we have 3 classes: A, B, C.

• Class A = 1000 samples
• Class B = 100 samples
• Class C = 50 samples
• If you compute Macro AUC: each class AUC gets equal weight (⅓).
• If you compute Micro AUC: class A dominates, since it has most samples.

If you care about overall performance weighted by data distribution → Micro AUC is appropriate.

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5) When to Use

• Micro AUC:
  • Good for imbalanced data when you want a sample-weighted global performance.
  • Answers: “How well does the model rank positives vs negatives overall?”
• Macro AUC:
  • Good if you want fairness across classes.
  • Answers: “How well does the model perform for each class, equally?”

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Summary

• Micro AUC = AUC computed after pooling predictions across all classes.
• Weights performance by class frequency.
• Contrast: Macro AUC averages per-class AUCs equally.
• Use Micro AUC for global sample-level performance, Macro AUC for class-level fairness.