ROC & PR Curve (Python)

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The ROC curve trades sensitivity against (1 − specificity) across every score threshold, summarized by AUC; the precision–recall curve exposes the same ranking from the positive-class perspective and is the honest display under heavy class imbalance. Both are one call from scikit-learn’s metric functions and one line of matplotlib styling.

Example

Setup

• System Requirements: Cross-platform (Linux/MacOS/Windows)
• Programming Language: Python
• Dependencies: matplotlib, seaborn, pandas, numpy, scikit-learn

import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
import numpy as np
from sklearn.metrics import roc_curve, auc, precision_recall_curve, average_precision_score

Data Preparation

We simulate diagnostic scores for 2,000 patients with a 10% prevalence: healthy scores centred at 0, diseased scores shifted upward — a useful-but-not-perfect classifier.

np.random.seed(161)

n, prevalence = 2000, 0.10
label = (np.random.random(n) < prevalence).astype(int)
scores = np.where(label == 1,
                  np.random.normal(0.9, 0.55, n),
                  np.random.normal(0.0, 0.65, n))

fpr, tpr, _ = roc_curve(label, scores)
roc_auc = auc(fpr, tpr)
prec, rec, _ = precision_recall_curve(label, scores)
ap = average_precision_score(label, scores)

Visualization

ROC Curve with AUC

The diagonal is the chance classifier; plotting each candidate model on the same axes turns model selection into one glance.

fig, ax = plt.subplots(figsize=(4.8, 4.8))
ax.plot(fpr, tpr, color='#e63946', linewidth=1.9,
        label=f'AUC = {roc_auc:.3f}')
ax.plot([0, 1], [0, 1], color='0.5', linewidth=0.9, linestyle='--',
        label='Chance')
ax.set_xlabel('False positive rate')
ax.set_ylabel('True positive rate')
ax.set_xlim(-0.02, 1.0)
ax.set_ylim(0, 1.02)
ax.legend(frameon=False, loc='lower right')
ax.spines[['top', 'right']].set_visible(False)
plt.tight_layout()
plt.show()

Figure 1: ROC curve with the chance diagonal and AUC

Precision–Recall Curve with Average Precision

With 10% prevalence the chance line sits at 0.10 (dashed) — an AUC that looks flattering on the ROC can look far less so here, which is exactly the point.

fig, ax = plt.subplots(figsize=(4.8, 4.8))
ax.plot(rec, prec, color='#457b9d', linewidth=1.9,
        label=f'AP = {ap:.3f}')
ax.axhline(prevalence, color='0.5', linewidth=0.9, linestyle='--',
           label=f'Prevalence = {prevalence:.2f}')
ax.set_xlabel('Recall')
ax.set_ylabel('Precision')
ax.set_xlim(0, 1.0)
ax.set_ylim(0, 1.02)
ax.legend(frameon=False, loc='upper right')
ax.spines[['top', 'right']].set_visible(False)
plt.tight_layout()
plt.show()

Figure 2: Precision-recall curve with average precision and prevalence baseline

References

1. Pedregosa, F., et al. (2011). Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12, 2825-2830.
2. Saito, T., & Rehmsmeier, M. (2015). The Precision-Recall Plot Is More Informative than the ROC Plot When Evaluating Binary Classifiers on Imbalanced Datasets. PLoS ONE, 10(3), e0118432.