Which evaluation metric is most appropriate for a highly imbalanced classification problem?

Question

BlackTom AI · Accepted Answer

In imbalanced classification, precision and recall are more informative than accuracy because they focus on the minority class performance.

1. Relevant knowledge points and concepts
- Accuracy = (TP + TN) / total; can be misleading when one class dominates.
- Precision = TP / (TP + FP): of predicted positives, how many are true.
- Recall (sensitivity) = TP / (TP + FN): of actual positives, how many are found.
- F1-score = 2 * (precision * recall) / (precision + recall): harmonic mean balancing precision and recall.
- R-squared and Mean Squared Error (MSE) are regression metrics, not suited for classification.

2. Step-by-step reasoning
- For imbalanced data the minority class (positive) is often most important; a model that always predicts the majority class can yield high accuracy but zero usefulness.
- F1-score directly combines precision and recall, so it penalizes models that miss many positives (low recall) or that produce many false positives (low precision).

3. Calculations with intermediate steps (numeric example)
- Suppose 100 samples: 95 negative, 5 positive. A naive classifier predicts all negative: TP=0, TN=95, FP=0, FN=5.
- Accuracy = (TP+TN)/100 = 95/100 = 0.95 (95%).
- Precision undefined (no predicted positives) or treated as 0; Recall = 0/5 = 0.
- F1 = 0 (because recall or precision is 0), showing the model is useless despite 95% accuracy.
- Another model: predicts 3 positives and all 3 are true: TP=3, FP=0, FN=2.
  Precision = 3/(3+0) = 1.0; Recall = 3/(3+2) = 0.6.
  F1 = 2*(1.0*0.6)/(1.0+0.6) = 1.2/1.6 = 0.75. This reflects genuine positive-class performance.

4. Why the correct answer is correct
- F1 penalizes imbalance-related failures by combining precision and recall; it reveals trade-offs and effectiveness on the minority class, which accuracy (or regression metrics) cannot.

5. Why other options are incorrect
- R-squared: regression goodness-of-fit; not for classification.
- Mean Squared Error: regression loss metric, inappropriate for discrete class labels.
- Accuracy: can be very high even if the model fails to detect the minority class; not reliable for imbalanced datasets.

6. Conclusion
- The most appropriate metric among the options for a highly imbalanced classification problem is F1-Score, which matches the provided answer.

Which evaluation metric is most appropriate for a highly imbalanced classification problem?单项选择题

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