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.

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.

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.

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.

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?”

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.