Area Under Precision-Recall Curve (AUPRC)
The Area Under the Precision-Recall Curve (AUPRC) is a single scalar value that summarizes the performance of a binary classification model by measuring the area under its Precision-Recall (PR) curve.
What is the Precision-Recall Curve?
The Precision-Recall Curve plots:
- Precision (y-axis): the proportion of true positive predictions among all positive predictions.
- Recall (x-axis): the proportion of true positives detected out of all actual positives.
Different classification thresholds produce different pairs of precision and recall, forming the PR curve.
What Does AUPRC Represent?
AUPRC quantifies the trade-off between precision and recall for all thresholds:
- A higher AUPRC means better performance in identifying positive samples correctly without too many false positives.
- It is especially useful in imbalanced datasets where the positive class is rare.
Mathematical Definition
Where Precision(r) is the precision value at recall level r.
Why Use AUPRC Instead of ROC AUC?
- ROC AUC evaluates trade-offs between True Positive Rate and False Positive Rate.
- When dealing with imbalanced data, ROC AUC can give an overly optimistic view.
- AUPRC focuses only on the positive class, providing a more informative metric for imbalanced problems.
Example
In a medical test for a rare disease:
- The model might have high ROC AUC but still produce many false alarms.
- AUPRC highlights how well the model balances identifying true disease cases (recall) and minimizing false alarms (precision).
Interpretation
- AUPRC = 1: Perfect precision and recall across thresholds.
- AUPRC ≈ positive class proportion: Baseline score (random guessing).
- Higher AUPRC values indicate better model performance on positive class.
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