View source for Area Under Precision-Recall Curve (AUPRC)

= 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 ==

:<math> \text{AUPRC} = \int_0^1 \text{Precision}(r) \, dr </math>

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.

== Related Pages ==

* [[Precision-Recall Curve]]
* [[Precision]]
* [[Recall]]
* [[ROC Curve]]
* [[AUC Score]]
* [[Imbalanced Data]]

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[[Category:Artificial Intelligence]]