# Why is Precision-Recall AUC different from Average Precision score?

I have been calculating the area under the Precision-Recall curve (AUPRC) using the code snippet below:

from sklearn import metrics

precision, recall, threshold = metrics.precision_recall_curve(y_true, y_pred)
prec_rec_auc_score = metrics.auc(recall, precision)


and the Average Precision (AP) by using the code below:

from sklearn import metrics

avg_precision_score = metrics.average_precision_score(y_true, y_pred)


The two scores have usually been exactly the same, however, I recently came across a situation where the area under the Precision-Recall curve (AUPRC) was significantly larger than the Average Precision (AP) score. Is this possible? And why would this happen?

• Welcome to here. Please check these posts about the difference between AUC of PR-curve & Average Precision (AP) or AUPRC vs. AUC-ROC. Do you mean why $$AUPRC >>AUPR$$ ? check this answer Sklearn Average_Precision_Score vs. AUC Jan 25 at 2:13
• My second question is are you using Imbalanced Datasets in your evaluation analysis? IS your task about anomaly/outlier detection? Jan 25 at 2:24
• Hi Mario! I believe $AUPRC$ and $AUPR$ are both the same thing, i.e. the area under the Precision-Recall curve, right? What I mean is that $AUPRC \gg AP$. And yes, I should have mentioned that my dataset is very imbalanced, but I've used the same dataset to calculate these metrics before (using different prediction methods) and ended up with the same result for both metrics ($AUPRC$ and $AP$) so I'm wondering why this time I end up with a difference in the $AUPRC$ and $AP$ scores. My task is binary forecasting. Jan 25 at 11:23

I have tried to generate a dataset with a 95:5 class imbalance, train a RandomForestClassifier model, and calculate AUPRC and AUC-ROC and Average Precision (AP) scores for the binary classification task:

My observations show that $$AP$$ is always slightly greater than $$AUPRC$$: $$AUPRC

There could be a chance that $$AUPRC>=AP$$ which could be reasoned in the interpolation method. doesn't explicitly document the interpolation method used in the precision_recall_curve and average_precision_score functions.

From the documentation states that:

average_precision_score function calculates the area under the precision-recall curve using the trapezoidal rule.

However, it doesn't explicitly mention the interpolation method used for precision-recall points. ref.

precision_recall_curve computes precision-recall pairs for different probability thresholds and uses linear interpolation to estimate precision values at different recall levels.

Python code:

import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import precision_recall_curve, auc, average_precision_score, roc_curve, roc_auc_score

# Generate imbalanced data with labels for positive (1) and negative (0) classes
X, y = make_classification(n_samples=1000, n_features=20, n_classes=2,
weights=[0.95, 0.05], random_state=42)

# Count the number of observations for each class
num_positive_class = np.sum(y == 1)
num_negative_class = np.sum(y == 0)

# Scatter plot for binary class distribution
plt.figure(figsize=(8, 8))
plt.scatter(X[y == 1, 0], X[y == 1, 1], c='blue', edgecolors='k', label=f'Positive Class (1): {num_positive_class}')
plt.scatter(X[y == 0, 0], X[y == 0, 1], c='red', edgecolors='k', label=f'Negative Class (0): {num_negative_class}')
plt.title('Binary Class Distribution')
plt.xlabel('Feature 1')
plt.ylabel('Feature 2')
plt.legend(loc='best')
plt.show()

# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Train a Random Forest classifier
model = RandomForestClassifier(random_state=42)
model.fit(X_train, y_train)

# Predict probabilities on the test set
y_proba = model.predict_proba(X_test)[:, 1]

# Calculate precision-recall curve
precision, recall, _ = precision_recall_curve(y_test, y_proba)

# Calculate AUPRC
auprc = auc(recall, precision)

# Calculate ROC curve
fpr, tpr, _ = roc_curve(y_test, y_proba)

# Calculate AUC-ROC
roc_auc = roc_auc_score(y_test, y_proba)

# Calculate Average Precision (AP) for the Random Forest model
ap_random_forest = average_precision_score(y_test, y_proba)

# Calculate chance level AP
ap_chance_level = np.sum(y_test) / len(y_test)

# Plot AUPRC, AUC-ROC, and AP in subplot 1x3
plt.figure(figsize=(18, 6))

# Plot AUPRC
plt.subplot(1, 3, 1)
plt.plot(recall, precision, label=f'Random Forest Model (AP={ap_random_forest:.4f})', color='orange')
plt.xlabel('Recall (Positive class: 1)')
plt.ylabel('Precision (Positive class: 1)')
plt.title('Precision-Recall Curve')
plt.axhline(y=ap_chance_level, color='red', linestyle='--', label=f'Chance Level (AP={ap_chance_level:.4f})')
plt.legend(loc='best')

# Plot AUC-ROC
plt.subplot(1, 3, 2)
plt.plot(fpr, tpr, label=f'AUC-ROC = {roc_auc:.4f}', color='green')
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('ROC Curve')
plt.legend(loc='best')

# Plot AP with annotation
plt.subplot(1, 3, 3)
bars = plt.bar([0, 1, 2], [auprc, roc_auc, ap_random_forest], tick_label=['AUPRC', 'AUC-ROC', 'AP'], color=['orange', 'green', 'blue'])
plt.ylim(0, 1)
plt.title('AUPRC, AUC-ROC, and Average Precision (AP)')

# Annotate values on top of bars with increased font size
for bar in bars:
yval = bar.get_height()
plt.text(bar.get_x() + bar.get_width()/2, yval, round(yval, 4), ha='center', va='bottom', fontsize=12)

plt.legend(loc='best')
plt.tight_layout()
plt.show()


I could not argue further but I also used LogisticRegression and changed the imbalance rate but the results didn't change and $$AUPRC (slightly).