What methods are available for choosing a threshold based on the ROC curve?

Choosing a threshold based on the ROC curve is an important step in tuning a binary classifier. Main methods for threshold selection:

1. Maximizing Youden's J statistic:

   • Calculated as J = Sensitivity + Specificity - 1.
   • The threshold is chosen where J is maximized, which corresponds to an optimal balance between sensitivity and specificity.

2. Minimizing the distance to the point (0,1):

   • On the ROC curve, the point (0,1) represents an ideal classifier.
   • The threshold that minimizes the Euclidean distance between a point on the curve and (0,1) is selected.

3. Dependence on business logic:

   • If it is more important to minimize false positives, a threshold with high specificity is chosen.
   • If it is more important not to miss positive cases, a threshold with high sensitivity is chosen.

4. Using F1-score or other metrics:

   • The threshold that maximizes F1-score, accuracy, recall, or another relevant metric is selected.

Example in Python using sklearn:

from sklearn.metrics import roc_curve

fpr, tpr, thresholds = roc_curve(y_true, y_scores)

# Maximizing Youden's J
J = tpr - fpr
ix = np.argmax(J)
best_threshold = thresholds[ix]